{\rtf1\ansi\ansicpg1252\uc1 \deff0\deflang1033\deflangfe1033{\fonttbl{\f0\froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f1\fswiss\fcharset0\fprq2{\*\panose 020b0604020202020204}Arial;}
{\f28\fswiss\fcharset0\fprq0{\*\panose 00000000000000000000}Helvetica-BoldOblique;}{\f166\froman\fcharset238\fprq2 Times New Roman CE;}{\f167\froman\fcharset204\fprq2 Times New Roman Cyr;}{\f169\froman\fcharset161\fprq2 Times New Roman Greek;}
{\f170\froman\fcharset162\fprq2 Times New Roman Tur;}{\f171\froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\f172\froman\fcharset178\fprq2 Times New Roman (Arabic);}{\f173\froman\fcharset186\fprq2 Times New Roman Baltic;}
{\f174\fswiss\fcharset238\fprq2 Arial CE;}{\f175\fswiss\fcharset204\fprq2 Arial Cyr;}{\f177\fswiss\fcharset161\fprq2 Arial Greek;}{\f178\fswiss\fcharset162\fprq2 Arial Tur;}{\f179\fswiss\fcharset177\fprq2 Arial (Hebrew);}
{\f180\fswiss\fcharset178\fprq2 Arial (Arabic);}{\f181\fswiss\fcharset186\fprq2 Arial Baltic;}}{\colortbl;\red0\green0\blue0;\red0\green0\blue255;\red0\green255\blue255;\red0\green255\blue0;\red255\green0\blue255;\red255\green0\blue0;
\red255\green255\blue0;\red255\green255\blue255;\red0\green0\blue128;\red0\green128\blue128;\red0\green128\blue0;\red128\green0\blue128;\red128\green0\blue0;\red128\green128\blue0;\red128\green128\blue128;\red192\green192\blue192;}{\stylesheet{
\ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 \snext0 Normal;}{\s2\qr \li0\ri0\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 
\b\fs32\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 \sbasedon0 \snext0 heading 2;}{\s3\ql \li0\ri0\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \b\fs44\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 \sbasedon0 \snext0 
heading 3;}{\*\cs10 \additive Default Paragraph Font;}{\s15\ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs44\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 \sbasedon0 \snext15 Body Text;}{
\s16\qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 \sbasedon0 \snext16 Body Text 2;}{\*\cs17 \additive \ul\cf2 \sbasedon10 Hyperlink;}{\*\cs18 
\additive \ul\cf12 \sbasedon10 FollowedHyperlink;}}{\*\listtable{\list\listtemplateid-996492244\listhybrid{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid1867648106
\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-360\li720\jclisttab\tx720 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname ;}\listid485438615}{\list\listtemplateid-1654111336\listhybrid{\listlevel\levelnfc0\levelnfcn0\leveljc0
\leveljcn0\levelfollow0\levelstartat11\levelspace0\levelindent0{\leveltext\leveltemplateid-136162234\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-390\li750\jclisttab\tx750 }{\listlevel\levelnfc4\levelnfcn4
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2
\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2
\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2
\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname ;}\listid589699795}
{\list\listtemplateid418681774\listhybrid{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat13\levelspace0\levelindent0{\leveltext\leveltemplateid1203437284\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 
\chshdng0\chcfpat1\chcbpat1\fbias0 \fi-390\li750\jclisttab\tx750 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr
\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname ;}\listid1113745283}{\list\listtemplateid-1126535572\listhybrid{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat13\levelspace0
\levelindent0{\leveltext\leveltemplateid1743688200\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-390\li750\jclisttab\tx750 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1
\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname ;}\listid1121411627}{\list\listtemplateid-1684501786\listhybrid
{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid-865203188\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-360\li720
\jclisttab\tx720 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440
\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160
\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880
\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600
\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320
\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040
\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760
\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480
\jclisttab\tx6480 }{\listname ;}\listid1378041497}{\list\listtemplateid901663518\listhybrid{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid1462540070
\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-360\li720\jclisttab\tx720 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'01.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li1440\jclisttab\tx1440 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext
\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname ;}\listid1562980094}{\list\listtemplateid-2114805430\listhybrid{\listlevel\levelnfc0\levelnfcn0
\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid-1175943182\'03(\'00);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-360\li720\jclisttab\tx720 }{\listlevel\levelnfc4
\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid1065769076\'03(\'01);}{\levelnumbers\'02;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1\fbias0 \fi-360\li1440\jclisttab\tx1440 }{\listlevel
\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'02.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li2160\jclisttab\tx2160 }{\listlevel
\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'03.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li2880\jclisttab\tx2880 }{\listlevel
\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'04.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li3600\jclisttab\tx3600 }{\listlevel
\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'05.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li4320\jclisttab\tx4320 }{\listlevel
\levelnfc0\levelnfcn0\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698703\'02\'06.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5040\jclisttab\tx5040 }{\listlevel
\levelnfc4\levelnfcn4\leveljc0\leveljcn0\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698713\'02\'07.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-360\li5760\jclisttab\tx5760 }{\listlevel
\levelnfc2\levelnfcn2\leveljc2\leveljcn2\levelfollow0\levelstartat1\levelspace0\levelindent0{\leveltext\leveltemplateid67698715\'02\'08.;}{\levelnumbers\'01;}\chbrdr\brdrnone\brdrcf1 \chshdng0\chcfpat1\chcbpat1 \fi-180\li6480\jclisttab\tx6480 }{\listname 
;}\listid2074499410}}{\*\listoverridetable{\listoverride\listid2074499410\listoverridecount0\ls1}{\listoverride\listid1562980094\listoverridecount0\ls2}{\listoverride\listid485438615\listoverridecount0\ls3}{\listoverride\listid589699795
\listoverridecount0\ls4}{\listoverride\listid1121411627\listoverridecount0\ls5}{\listoverride\listid1113745283\listoverridecount0\ls6}{\listoverride\listid1378041497\listoverridecount0\ls7}}{\info{\title  }{\author IST}{\operator Tony CRUTTENDEN}
{\creatim\yr2002\mo3\dy4\hr19\min10}{\revtim\yr2002\mo3\dy4\hr19\min10}{\version2}{\edmins48}{\nofpages2}{\nofwords575}{\nofchars3280}{\*\company International School of Toulouse}{\nofcharsws4028}{\vern8247}}\margl1985\margr567\margt1985\margb1134 
\widowctrl\ftnbj\aenddoc\noxlattoyen\expshrtn\noultrlspc\dntblnsbdb\nospaceforul\formshade\horzdoc\dgmargin\dghspace120\dgvspace180\dghorigin1985\dgvorigin1985\dghshow2\dgvshow2
\jexpand\viewkind1\viewscale100\pgbrdrhead\pgbrdrfoot\splytwnine\ftnlytwnine\htmautsp\nolnhtadjtbl\useltbaln\alntblind\lytcalctblwd\lyttblrtgr\lnbrkrule \fet0\sectd \linex0\headery851\endnhere\sectlinegrid360\sectdefaultcl {\*\pnseclvl1
\pnucrm\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl2\pnucltr\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang{\pntxta .}}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang{\pntxta )}}{\*\pnseclvl5
\pndec\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl6\pnlcltr\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl7\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl8\pnlcltr\pnstart1\pnindent720\pnhang
{\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}\trowd \trgaph108\trleft-120\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth1\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1320 \cellx1200
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7920 \cellx9120\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\fs44\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\b\i {\*\shppict{\pict{\*\picprop\shplid1025{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pibName}{\sv IST-logo-v_little-6
.gif}}{\sp{\sn pibFlags}{\sv 2}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex312\picscaley300\piccropl0\piccropr0\piccropt0\piccropb0
\picw582\pich794\picwgoal330\pichgoal450\pngblip\bliptag-1168354149{\*\blipuid ba5c549b13b3e4220419d020dd8dd68e}89504e470d0a1a0a0000000d49484452000000160000001e08030000001f391e6400000300504c5445ffffff1818182929293131313939394242424a4a4a5252
525a5a5a6363636b6b6b7373737b7b7b8484848c8c8c9494949c9c9ca5a5a5adadadb5b5b5bdbdbd000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000c0c0c033171e060000010074524e53ffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0053f7072500000001624b47
44ffa507f2c5000000ad49444154789c6dd05b0ec420080550a70f51c45ac5fd6f95199b4cd5167f302704c83532be5aaf826246653a5b219ab8c6949ba24c7c
84c4c21eebccc9154996da779a2d05b66bfac835e16767993993f516aa0c5c1202603e80ff4da61ce8c0c75c85f7720f3427356acf53dfd357f2c61a472b1a3b
541974c64d655e82c692d77ef894b75f4e857f89afcfa8e6731e4c56e5002adba031eb2bd16907e63bdb91793fe4cd05a2bc9943ea2d5fbe9d1c01f1ec80080000000049454e44ae426082}}{\nonshppict{\pict\picscalex314\picscaley300\piccropl0\piccropr0\piccropt0\piccropb0
\picw582\pich794\picwgoal330\pichgoal450\wmetafile8\bliptag-1168354149{\*\blipuid ba5c549b13b3e4220419d020dd8dd68e}0100090000030e04000000008a03000000000400000003010800050000000b0200000000050000000c021e001600040000000701040062000000430f8600ee00
00001e001600000000001e0016000000000028000000160000001e000000010001000000000078000000c40e0000c40e0000020000000200000000000000ffff
ff00007000ff003800ff001c00ff000e00ff000600ff000700ff000300ff000300ff000300ff000300ff000700ff001e00ff003c00ff007000ff006000ff0060
00ff006000ff006000ff007000fff83000ffffb800ff0ffc00ff00fe00ff003f00ff000780ff001dc0ff001ef0ff001e30ff000e18ff000608ff8a030000430f
c600880000001e001600000000001e0016000000000028000000160000001e000000010008000000000048030000c40e0000c40e000000010000170000000000
000018181800292929003131310039393900424242004a4a4a00525252005a5a5a00636363006b6b6b00737373007b7b7b00848484008c8c8c00949494009c9c
9c00a5a5a500adadad00b5b5b500bdbdbd00c0c0c000ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffffff00ffff
ffffffffffffff140b10ffffffffffffffffffff0301ffffffffffffffffffff12070dffffffffffffffffff0400ffffffffffffffffffffff140310ffffffff
ffffffff0000ffffffffffffffffffffffff120315ffffffffffffff0100ffffffffffffffffffffffffff0907ffffffffffffff0200ffffffffffffffffffff
ffffff140314ffffffffffff000effffffffffffffffffffffffffff050bffffffffffff0003ffffffffffffffffffffffffffff0b07ffffffffffff0060ffff
ffffffffffffffffffffffff0d05ffffffffffff0ffcffffffffffffffffffffffffffff0709ffffffffffff001effffffffffffffffffffffffff0d0214ffff
ffffffff1e00ffffffffffffffffffffff14090210ffffffffffffff1e00ffffffffffffffffffff12030512ffffffffffffffff0001ffffffffffffffffff14
020bffffffffffffffffffff3939ffffffffffffffffff0905ffffffffffffffffffffff6b6bffffffffffffffffff0709ffffffffffffffffffffff9c9cffff
ffffffffffffff0909ffffffffffffffffffffffffffffffffffffffffffff0d05ffffffffffffffffffffffffffffffffffffffffffff140314ffffffffffff
ffffffffffff100b0d1214ffffffffff090bffffffffffffffffffffffff1210090707090d1214ff140514ffffffffffffffffffffffffffffff12100907070b
120d0714ffffffffffffffffffffffffffffffffffff120b0509050714ffffffffffffffffffffffffffffffffffffff141009010514ffffffffffffffffffff
ffffffffffffffffffffff12070312ffffffffffffffffffffffffffffffffffff100714ff0d050bffffffffffffffffffffffffffffffffff0d0b0d14ff1409
0b15ffffffffffffffffffffffffffffff140d1012ffffff0b09ffffffffffffffffffffffffffffffff140b10ffffffff0d0bffffffffffffffffffffffffffffffff1414ffffffffff09ffffff0400000007010100030000000000}}}{\fs40 \cell }{\i\fs28 
The International School of Toulouse Department of Mathematics. 
\par }\pard\plain \s3\ql \li0\ri0\keepn\widctlpar\intbl\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0 \b\fs44\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\fs28 Math Higher Portfolio assignment \endash  Modelling Coins}{\b0 
\par }\pard\plain \s2\qr \li0\ri0\keepn\widctlpar\intbl\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0 \b\fs32\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {TYPE III\cell }\pard\plain 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\trowd \trgaph108\trleft-120\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 
\trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trftsWidthB3\trftsWidthA3\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1320 \cellx1200\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth7920 \cellx9120\row }\pard 
\ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {
\par }{\b\i\f28\lang1033\langfe1033\langnp1033 Work done in this assignment will be assessed against the criteria A, B, C, D and F. You are therefore expected to use a graphic display calculator/computer for this assignment.
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\fs20\ul\lang1024\langfe1024\noproof\langnp1033 
{\shp{\*\shpinst\shpleft-120\shptop317\shpright9480\shpbottom1522\shpfhdr0\shpbxcolumn\shpbxignore\shpbypara\shpbyignore\shpwr3\shpwrk0\shpfblwtxt0\shpz0\shplid1026{\sp{\sn shapeType}{\sv 1}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}
{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}{\shprslt{\*\do\dobxcolumn\dobypara\dodhgt0\dprect\dpx-120\dpy317\dpxsize9600\dpysize1205
\dpfillfgcr255\dpfillfgcg255\dpfillfgcb255\dpfillbgcr255\dpfillbgcg255\dpfillbgcb255\dpfillpat1\dplinew15\dplinecor0\dplinecog0\dplinecob0}}}}{\b\ul\lang1033\langfe1033\langnp1033 
\par }\pard \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {Alex has a coin with a '1' on one side and a '3' on the other. Beth's coin has a '2' on both sides. \line Each player begins with a starting value of  }
{\f1\fs20 1}{.\line They multiply the starting value by the number they throw on their respective coins.
\par }\pard\plain \s16\qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\lang1033\langfe1033\langnp1033 
\par }\pard\plain \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\b\ul\lang1033\langfe1033\langnp1033 Section One; The original game;
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (1)\tab}}\pard \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 {
After many games, do you expect that the outcome will be: \line          (a) Alex gets a higher score than Beth?\line          (b) Beth gets a higher score than Alex?\line          (c) They both average the same score?}{\lang1033\langfe1033\langnp1033 
\tab 
\par }\pard \ql \li720\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin720\itap0 {\lang1033\langfe1033\langnp1033 Give reasons for your answer.
\par {\listtext\pard\plain\hich\af0\dbch\af0\loch\f0 (2)\tab}}\pard \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 {\lang1033\langfe1033\langnp1033 
Play the game with 10 trials for yourself a few times and record your results.
\par {\listtext\pard\plain\hich\af0\dbch\af0\loch\f0 (3)\tab}Collect Data from the }{\b\lang1033\langfe1033\langnp1033 Intro }{\lang1033\langfe1033\langnp1033 page of the }{\field{\*\fldinst {\lang1033\langfe1033\langnp1033 
 HYPERLINK "http://www.planetqhe.com/frames/comp2frames.html" }{\lang1033\langfe1033\langnp1033 {\*\datafield 
00d0c9ea79f9bace118c8200aa004ba90b0200000003000000e0c9ea79f9bace118c8200aa004ba90b6200000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00
650073002e00680074006d006c000000}}}{\fldrslt {\cs17\ul\cf2\lang1033\langfe1033\langnp1033 Alex and Beth spreadsheet}}}{\lang1033\langfe1033\langnp1033 , where you can simulate 20 trials of this game. Also try the }{\b\lang1033\langfe1033\langnp1033 
100 trials}{\lang1033\langfe1033\langnp1033  page.
\par {\listtext\pard\plain\hich\af0\dbch\af0\loch\f0 (4)\tab}Comment on the results of your experiments in parts (2) and (3) and how they relate to your initial idea in (1).
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\ul\lang1033\langfe1033\langnp1033 Section Two; Comparing the Expectations;}{
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (5)\tab}}\pard \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 {Suppose that Alex and Beth
 pay the game for }{\i n}{ trials. Let }{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb
\objw859\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c0000000000000460000000000000000000000008072
51eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c0000000200d8d82c00000000000000bc804900e48249000000000003010103010a0112834500030f01000b01128342000011000a02822800128378000282290002863d00000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400eb050000a8fdffff180200000800eb0558020000
010009000003070100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02200260051200000026060f001a00ffffffff000010000000c0ffffffa6ffffff20050000c60100000b0000002606
0f000c004d617468547970650000500010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320a80014304010000003d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000
f001000008000000320a80015f0301000000290008000000320a80010f0201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a8001ab0201000000780008000000320a80014600010000004500
15000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f001000008000000320ae00148010100000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000
040000002d01000004000000f00101000300000000000000}{\result {\dn10 {\pict{\*\picprop\shplid1026{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1515\pich600\picwgoal859\pichgoal340\wmetafile8\bliptag1736989867\blipupi2305{\*\blipuid 67885cabe6d3306f0ff12e13d29cc900}010009000003070100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02200260051200000026060f001a00ffffffff000010000000c0ffffffa6ffffff20050000c60100000b00000026060f00
0c004d617468547970650000500010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320a80014304
010000003d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f0010000
08000000320a80015f0301000000290008000000320a80010f0201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01000004000000f001010008000000320a8001ab0201000000780008000000320a8001460001000000450015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f001000008000000320ae00148010100
000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{the expected value of Beth\rquote s winnings after }{\i n}{ trials. Show that }{\pard\plain 
\ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1120\objh360{\*\objclass Equation.3}
{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c0000000000000460000000000000000000000008072
51eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c0000000200d8d83c00000000000000e48f490008a549000000000003010103010a0112834500030f01000b01128342000011000a02822800128378000282290002863d0002883200030f00000b110112836e00000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000058000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400b807000085fdffff380200000800b8077b020000
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02400200071200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0060000f70100000b0000002606
0f000c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a4040000002d01000008000000320af4005606010000006e0008000000320a0002480101000000420015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e0000a4040000002d01010004000000f001000008000000320aa001ab0201000000780008000000320aa001460001000000450015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a4040000002d01000004000000f001010008000000320a
a0017b0501000000320008000000320aa0015f0301000000290008000000320aa0010f0201000000280010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320aa0014304010000003d000a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000ffff}{\result {\dn10 {\pict{\*\picprop\shplid1027{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1976\pich635\picwgoal1120\pichgoal360\wmetafile8\bliptag-1848086045\blipupi-2266{\*\blipuid 91d871e35d488915019e012327f79d33}
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02400200071200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0060000f70100000b00000026060f00
0c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a4040000002d010000
08000000320af4005606010000006e0008000000320a0002480101000000420015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000a4040000002d01010004000000f001000008000000320aa001ab0201000000780008000000320aa001460001000000450015000000fb02
80fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a4040000002d01000004000000f001010008000000320aa0017b050100
0000320008000000320aa0015f0301000000290008000000320aa0010f0201000000280010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320aa0014304010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (6)\tab}A table for the probability distribution of Alex\rquote s winnings after one trial is;
\par }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\pard \qc \li0\ri0\sa120\sl-320\slmult0
\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {a\cell 1\cell 3\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\row }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\pard \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\pard\plain \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1080\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000a013
59eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb3000000000000000bc804900e48249000000000003010103010a0112835000030f01000b01128341000011000a028228001283580002863d0012836100028229000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
000000000000000000000000000000000000000000000000000000000000040000004c000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540071070000a8fdffff280200000800710758020000
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01
000004000000f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02
000000000102022253797374656d0000040000002d01000004000000f00101000300000000000000}{\result {\dn10 {\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1905\pich600\picwgoal1080\pichgoal340\wmetafile8\bliptag-747796703\blipupi2304{\*\blipuid d36d8721b01db3b85d823b2f13a275cb}
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a
8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000
f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{\cell \'bd\cell \'bd\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400
\row }\pard \ql \li360\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {Show that the probability distribution of Alex\rquote s winnings after two trials is;
\par }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\pard \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {a\cell 1\cell 3\cell 9\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\row }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\pard 
\qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\pard\plain \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 
\fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1080\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000603b
62eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb3000000000000000bc804900e48249000000000003010103010a0112835000030f01000b01128341000011000a028228001283580002863d0012836100028229000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
000000000000000000000000000000000000000000000000000000000000040000004c000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540071070000a8fdffff280200000800710758020000
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01
000004000000f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02
000000000102022253797374656d0000040000002d01000004000000f00101000300000000000000}{\result {\dn10 {\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1905\pich600\picwgoal1080\pichgoal340\wmetafile8\bliptag-747796703\blipupi2304{\*\blipuid d36d8721b01db3b85d823b2f13a275cb}
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a
8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000
f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{\cell \'bc\cell 2/4\cell 1/4\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\row }\pard \ql \li360\ri0\sa120\sl-320\slmult0
\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 { 
\par And show that the probability distribution of Alex\rquote s winnings after three trials is;
\par }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx9240\pard 
\qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {a\cell 1\cell 3\cell 9\cell 27\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt
\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt
\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx9240\row }\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx9240\pard \qc \li0\ri0\sa120\sl-320\slmult0
\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\pard\plain \qc \li0\ri0\sa120\sl-320\slmult0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb
\objw1080\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000080dc
69eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb3000000000000000bc804900e48249000000000003010103010a0112835000030f01000b01128341000011000a028228001283580002863d0012836100028229000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
000000000000000000000000000000000000000000000000000000000000040000004c000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540071070000a8fdffff280200000800710758020000
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01
000004000000f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02
000000000102022253797374656d0000040000002d01000004000000f00101000300000000000000}{\result {\dn10 {\pict{\*\picprop\shplid1030{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1905\pich600\picwgoal1080\pichgoal340\wmetafile8\bliptag-747796703\blipupi2304{\*\blipuid d36d8721b01db3b85d823b2f13a275cb}
0100090000030f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002c0061200000026060f001a00ffffffff000010000000c0ffffffa6ffffff80060000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a80010a0601000000290008000000320a8001d20101000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a80013e0501000000610008000000320a80017a0201000000580008000000320a
8001460001000000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000
f001010008000000320ae001160101000000410010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000
f001000008000000320a80010604010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{\cell 1/8\cell 3/8\cell 3/8\cell 1/8\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\trowd \trqc\trgaph108\trleft252\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trautofit1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1548 \cellx1800\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1680 \cellx3480\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx5400
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1920 \cellx7320\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1920 \cellx9240\row }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (7)\tab}}\pard \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 {Let }{\pard\plain 
\ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw660\objh340{\*\objclass Equation.3}
{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000080dc
69eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020074cf2800000000000000bc804900e48249000000000003010103010a0112834500030f01000b01128341000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c4550494354008c040000a8fdffffd801000008008c0458020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02200220041200000026060f001a00ffffffff000010000000c0ffffffa6ffffffe0030000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a80015f0301000000290008000000320a80010f0201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a8001ab0201000000780008000000320a8001460001000000450015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a
e00153010100000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f00100000300000000000100}{\result {\dn10 
{\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1164\pich600\picwgoal660\pichgoal340\wmetafile8\bliptag2089027675\blipupi2305{\*\blipuid 7c84085b217afd2098899b49f0962369}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02200220041200000026060f001a00ffffffff000010000000c0ffffffa6ffffffe0030000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a80015f0301000000290008000000320a80010f0201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a8001ab0201000000780008000000320a8001460001000000450015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320ae00153010100
000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{denote the expected value of Alex\rquote s winnings after }{\i n}{
 trials. Prove using the binomial theorem or otherwise that }{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 
\fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1120\objh360{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000080dc
69eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c0000000200d4d73c00000000000000bc804900e48249000000000003010103010a0112834500030f01000b01128341000011000a02822800128378000282290002863d0002883200030f00000b110112836e00000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000058000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400b807000085fdffff380200000800b8077b020000
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02400200071200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0060000f70100000b0000002606
0f000c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320af4005606010000006e0008000000320a0002530101000000410015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320aa001ab0201000000780008000000320aa001460001000000450015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a
a0017b0501000000320008000000320aa0015f0301000000290008000000320aa0010f0201000000280010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320aa0014304010000003d000a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000ffff}{\result {\dn10 {\pict{\*\picprop\shplid1032{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1976\pich635\picwgoal1120\pichgoal360\wmetafile8\bliptag-2136294905\blipupi-2266{\*\blipuid 80aaba074aba166ca83515b9848ef051}
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02400200071200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0060000f70100000b00000026060f00
0c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320af4005606010000006e0008000000320a0002530101000000410015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320aa001ab0201000000780008000000320aa001460001000000450015000000fb02
80fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320aa0017b050100
0000320008000000320aa0015f0301000000290008000000320aa0010f0201000000280010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320aa0014304010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{.
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (8)\tab}Compare, for }{\i n}{ trials, the shape of the distributions of }{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar
\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1900\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
00000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c0000000000000460000000000000000000000004004
73eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb5400000000000000848e4900cca549000000000003010103010a0112836600030f01000b01128341000011000a02822800128378000282290002863d0012835000030f01000b01128341000011000a028228
001283580002863d00128361000282290000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400170d0000a8fdffff880200000800170d58020000
0100090000033f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002e00b1200000026060f001a00ffffffff000010000000c0ffffffa6ffffffa00b0000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000b5040000002d01000008000000320a80011b0b01000000290008000000320a8001e30601000000280008000000320a80012e0301000000290008000000320a8001de010100
0000280015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e0000b5040000002d01010004000000f001000008000000320a80014f0a01000000610008000000320a80018b0701000000580008000000320a8001560501000000500008000000320a80017a02010000007800
08000000320a8001820001000000660015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000b5040000002d01000004000000f001010008000000320ae001270601000000410008000000320ae001220101000000410010000000fb0280fe000000000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320a80011709010000003d0008000000320a80011204010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f001
0100030000000000ffff}{\result {\dn10 {\pict{\*\picprop\shplid1033{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3351\pich600\picwgoal1900\pichgoal340\wmetafile8\bliptag-255679665\blipupi-715{\*\blipuid f0c2a34fc48a56e8239b74176b1b9c61}
0100090000033f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002e00b1200000026060f001a00ffffffff000010000000c0ffffffa6ffffffa00b0000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000b5040000002d010000
08000000320a80011b0b01000000290008000000320a8001e30601000000280008000000320a80012e0301000000290008000000320a8001de01010000002800
15000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e0000b5040000002d01010004000000f001000008000000320a
80014f0a01000000610008000000320a80018b0701000000580008000000320a8001560501000000500008000000320a80017a0201000000780008000000320a
8001820001000000660015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000b5040000002d01000004000000
f001010008000000320ae001270601000000410008000000320ae001220101000000410010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a80011709010000003d0008000000320a80011204010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}
}}}{and }{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1880\objh340
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c0000000000000460000000000000000000000004004
73eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb54000000000000002c714900ec8b49000000000003010103010a0112836600030f01000b01128342000011000a02822800128378000282290002863d0012835000030f01000b01128342000011000a028228
001283580002863d00128362000282290000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400f40c0000a8fdffff880200000800f40c58020000
0100090000033f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002c00b1200000026060f001a00ffffffff000010000000c0ffffffa6ffffff800b0000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000cc040000002d01000008000000320a8001060b01000000290008000000320a8001e00601000000280008000000320a80012d0301000000290008000000320a8001dd010100
0000280015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e0000cc040000002d01010004000000f001000008000000320a8001400a01000000620008000000320a8001880701000000580008000000320a8001550501000000500008000000320a80017902010000007800
08000000320a8001820001000000660015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000cc040000002d01000004000000f001010008000000320ae0011a0601000000420008000000320ae001170101000000420010000000fb0280fe000000000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320a80011409010000003d0008000000320a80011104010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f001
0100030000000000ffff}{\result {\dn10 {\pict{\*\picprop\shplid1034{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3316\pich600\picwgoal1880\pichgoal340\wmetafile8\bliptag-1871809724\blipupi-742{\*\blipuid 906e734425ec531351b306c08bd3dc32}
0100090000033f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002c00b1200000026060f001a00ffffffff000010000000c0ffffffa6ffffff800b0000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000cc040000002d010000
08000000320a8001060b01000000290008000000320a8001e00601000000280008000000320a80012d0301000000290008000000320a8001dd01010000002800
15000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e0000cc040000002d01010004000000f001000008000000320a
8001400a01000000620008000000320a8001880701000000580008000000320a8001550501000000500008000000320a8001790201000000780008000000320a
8001820001000000660015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000cc040000002d01000004000000
f001010008000000320ae0011a0601000000420008000000320ae001170101000000420010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a80011409010000003d0008000000320a80011104010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}
}}}{ by using a spreadsheet. Hence comment on the limitations of the application of the formula }{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 
\fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw2100\objh400{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c0000000000000460000000000000000000000004004
73eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c0000000200d4d74800000000000000bc804900e48249000000000003010103010a011283450002822800128378000282290002863d00031d0200011283780012835000028228001283580002863d001283780002822900000b
11110d028611220000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000064000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400780e00003efdffff6c0200000800780ec2020000
010009000003320100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c028002200d1200000026060f001a00ffffffff000010000000c0ffffffaeffffffe00c00002e0200000b0000002606
0f000c004d617468547970650000700010000000fb02c0fd0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320af901b10401000000e50010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320a
a001630a010000003d0008000000320aa0017c03010000003d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320aa001610c01000000290008000000320aa0012f0801000000280008000000320aa0019802
01000000290008000000320aa001480101000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f001000008000000320aa001ad0b01000000780008000000320aa001d70801000000580008000000320aa001910602000000
785008000000320aa001e40101000000780008000000320aa00146000100000045000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}{\result {\dn14 
{\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3704\pich706\picwgoal2100\pichgoal400\wmetafile8\bliptag-107912135\blipupi-401{\*\blipuid f991643911cc551b2bdcfdaf2fff5dc3}
010009000003320100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c028002200d1200000026060f001a00ffffffff000010000000c0ffffffaeffffffe00c00002e0200000b00000026060f00
0c004d617468547970650000700010000000fb02c0fd0000000000009001000000020002001053796d626f6c0002040000002d01000008000000320af901b104
01000000e50010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320aa001630a
010000003d0008000000320aa0017c03010000003d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080
040000002d01000004000000f001010008000000320aa001610c01000000290008000000320aa0012f0801000000280008000000320aa0019802010000002900
08000000320aa001480101000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01
010004000000f001000008000000320aa001ad0b01000000780008000000320aa001d70801000000580008000000320aa001910602000000785008000000320a
a001e40101000000780008000000320aa00146000100000045000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{ as a measure of the }{\i expected winner}{
 in this coin game. What other measure of central tendency would be more appropriate? Why?
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\ul\lang1033\langfe1033\langnp1033 Section Two; Modelling the expected winner;}{
\par {\listtext\pard\plain\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 (9)\tab}}\pard \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 { Let }{\pard\plain 
\ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw740\objh340{\*\objclass Equation.3}
{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000060a5
7aeca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb2800000000000000bc804900e48249000000000003010103010a0112834d00030f01000b01128342000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540019050000a8fdffffd80100000800190558020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a8001d60301000000290008000000320a8001860201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a8001220301000000780008000000320a80014000010000004d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a
e001c0010100000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000320a}{\result {\dn10 
{\pict{\*\picprop\shplid1036{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1305\pich600\picwgoal740\pichgoal340\wmetafile8\bliptag-594711743\blipupi2305{\*\blipuid dc8d6b41601c43c9bbcff29f5c62e96f}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a8001d60301000000290008000000320a8001860201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a8001220301000000780008000000320a80014000010000004d0015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320ae001c0010100
000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{denote the median value of Beth\rquote s winnings after }{\i n}{ trials. Show that }
{\pard\plain \ql \fi-360\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls2\adjustright\rin0\lin720\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw1200\objh360{\*\objclass Equation.3}
{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000060a5
7aeca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb3c00000000000000bc804900e48249000000000003010103010a0112834d00030f01000b01128342000011000a02822800128378000282290002863d0002883200030f00000b110112836e00000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000058000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c4550494354004508000085fdffff38020000080045087b020000
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02400280071200000026060f001a00ffffffff000010000000c0ffffffb7ffffff40070000f70100000b0000002606
0f000c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320af400ce06010000006e0008000000320a0002c00101000000420015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320aa001230301000000780008000000320aa0014000010000004d0015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a
a001f30501000000320008000000320aa001d70301000000290008000000320aa001870201000000280010000000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000000f001000008000000320aa001bb04010000003d000a00000026060f000a00ffffffff010000000000
10000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000ffff}{\result {\dn10 {\pict{\*\picprop\shplid1037{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}
{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2117\pich635\picwgoal1200\pichgoal360\wmetafile8\bliptag-117853987\blipupi-2032{\*\blipuid f8f9b0dd9cde0bed4bd2a7a177136501}
010009000003170100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02400280071200000026060f001a00ffffffff000010000000c0ffffffb7ffffff40070000f70100000b00000026060f00
0c004d617468547970650000500015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320af400ce06010000006e0008000000320a0002c00101000000420015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320aa001230301000000780008000000320aa0014000010000004d0015000000fb02
80fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320aa001f3050100
0000320008000000320aa001d70301000000290008000000320aa001870201000000280010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320aa001bb04010000003d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01000004000000f0010100030000000000}}}}}{
\par }\pard \ql \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {(10) Let }{\pard\plain \ql \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 
{\object\objemb\objw740\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000060a5
7aeca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb2800000000000000e48f4900886d49000000000003010103010a0112834d00030f01000b01128341000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540019050000a8fdffffd80100000800190558020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d01000008000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320a
e001cb010100000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f00100000300000000000000}{\result {\dn10 
{\pict{\*\picprop\shplid1038{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1305\pich600\picwgoal740\pichgoal340\wmetafile8\bliptag657646808\blipupi2305{\*\blipuid 2732e4d87fb678edd2a920827e13b528}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d010000
08000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320ae001cb010100
000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{denote the median value of Alex\rquote s winnings after }{\i n}{
 trials with coin [1,3]. Show that 
\par }\pard \qc \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\pard\plain \qc \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb
\objw3040\objh999{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000e0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000feffffff05000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000020cd
83eca7c3c10103000000400200000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000060000000700000008000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb1c01000000000000bc804900e48249000000000003010103010a0112834d00030f01000b01128341000011000a02822800128378000282290002863d00030201000105010101020100000102883300030f00
000b1101030e00000112836e000286122202883100000102883200000000000a02822a0002883200000102883300030f00000b1101030e00000112836e00000102883200000000000000000a02967b000005010101020100000102812c000281200002812000028120000281200002812000028120000281200002812000
0281200002816e000281200002816f000281640002816400000102812c00028120000281200002814500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000038010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000200002812000028120000281200002812000028120000281200002816e000281200002816500028176000281650002816e0000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400f21400001ef9ffff480400000800f214e2060000
0100090000031f0200000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02400600131200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0120000f70500000b0000002606
0f000c004d617468547970650000600109000000fa02000008000000000000002200040000002d0100000500000014026e0179070500000013026e01db080500000014021904d8080500000013021904620915000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000800400
00002d01010009000000320aa604e30f040000006576656e08000000320aa604cf0e020000006e200c000000320aa604750b090000002020202020202020200008000000320aa604270b010000002c0009000000320a66022b10030000006f64640008000000320a6602170f020000006e200c000000320a6602bd0b0900
00002020202020202020200008000000320a66026f0b010000002c0008000000320a7d05060801000000330008000000320ad202430a01000000320008000000320ad2024d09010000002a0008000000320ad202a70601000000330008000000320a8003d70301000000290008000000320a800387020100000028001500
0000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01020004000000f001010008000000320a0505e90801000000320008000000320a5a02f60701000000320008000000320a1401750801000000310010000000fb0280fe0000000000009001000000020002
001053796d626f6c0002040000002d01010004000000f001020008000000320a3205f30501000000ef0008000000320ad905f30501000000ee0008000000320aa202f30501000000ef0008000000320ac203f30501000000ed0008000000320aab01f30501000000ec0008000000320a8003bb04010000003d0010000000
fb0220ff0000000000009001000000020002001053796d626f6c0002040000002d01020004000000f001010008000000320a14010608010000002d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f001020008000000320abf03
e708010000006e0008000000320a14018807010000006e0008000000320ae003cb0101000000410015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01020004000000f001010008000000320a8003230301000000780008000000320a800340000100
00004d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f00102000300000000000000}{\result {\dn44 
{\pict{\*\picprop\shplid1039{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw5362\pich1762\picwgoal3040\pichgoal999\wmetafile8\bliptag-378466049\blipupi629{\*\blipuid e97110fffe428657e1d762db17c568b8}
0100090000031f0200000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02400600131200000026060f001a00ffffffff000010000000c0ffffffb7ffffffc0120000f70500000b00000026060f00
0c004d617468547970650000600109000000fa02000008000000000000002200040000002d0100000500000014026e0179070500000013026e01db0805000000
14021904d8080500000013021904620915000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01
010009000000320aa604e30f040000006576656e08000000320aa604cf0e020000006e200c000000320aa604750b090000002020202020202020200008000000
320aa604270b010000002c0009000000320a66022b10030000006f64640008000000320a6602170f020000006e200c000000320a6602bd0b0900000020202020
20202020200008000000320a66026f0b010000002c0008000000320a7d05060801000000330008000000320ad202430a01000000320008000000320ad2024d09
010000002a0008000000320ad202a70601000000330008000000320a8003d70301000000290008000000320a8003870201000000280015000000fb0220ff0000
000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01020004000000f001010008000000320a0505e908010000003200
08000000320a5a02f60701000000320008000000320a1401750801000000310010000000fb0280fe0000000000009001000000020002001053796d626f6c0002
040000002d01010004000000f001020008000000320a3205f30501000000ef0008000000320ad905f30501000000ee0008000000320aa202f30501000000ef00
08000000320ac203f30501000000ed0008000000320aab01f30501000000ec0008000000320a8003bb04010000003d0010000000fb0220ff0000000000009001
000000020002001053796d626f6c0002040000002d01020004000000f001010008000000320a14010608010000002d0015000000fb0220ff0000000000009001
010000000402001054696d6573204e657720526f6d616e000080040000002d01010004000000f001020008000000320abf03e708010000006e0008000000320a
14018807010000006e0008000000320ae003cb0101000000410015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e000080040000002d01020004000000f001010008000000320a8003230301000000780008000000320a80034000010000004d000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010200030000000000}}
}}}{\lang1033\langfe1033\langnp1033 
\par }\pard \ql \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang1033\langfe1033\langnp1033 (11) Use a spreadsheet to compare the values of }{\pard\plain 
\ql \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw740\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
00000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000020cd
83eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb2800000000000000bc804900e48249000000000003010103010a0112834d00030f01000b01128342000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540019050000a8fdffffd80100000800190558020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d01000008000000320a8001d60301000000290008000000320a8001860201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e000080040000002d01010004000000f001000008000000320a8001220301000000780008000000320a80014000010000004d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320a
e001c0010100000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000a706}{\result {\dn10 
{\pict{\*\picprop\shplid1040{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1305\pich600\picwgoal740\pichgoal340\wmetafile8\bliptag-594711743\blipupi2305{\*\blipuid dc8d6b41601c43c9bbcff29f5c62e96f}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e000080040000002d010000
08000000320a8001d60301000000290008000000320a8001860201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000080040000002d01010004000000f001000008000000320a8001220301000000780008000000320a80014000010000004d0015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e000080040000002d01000004000000f001010008000000320ae001c0010100
000042000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{ and }{\pard\plain 
\ql \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw740\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e330000000000
00000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000020cd
83eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb2800000000000000e48f4900886d49000000000003010103010a0112834d00030f01000b01128341000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540019050000a8fdffffd80100000800190558020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d01000008000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320a
e001cb010100000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000a706}{\result {\dn10 
{\pict{\*\picprop\shplid1041{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1305\pich600\picwgoal740\pichgoal340\wmetafile8\bliptag657646808\blipupi2305{\*\blipuid 2732e4d87fb678edd2a920827e13b528}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d010000
08000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320ae001cb010100
000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{for n =1...20.
\par }\pard \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\b\ul\lang1033\langfe1033\langnp1033 Section Three; Making the game fair;
\par }\pard \ql \li360\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang1033\langfe1033\langnp1033 (12) There are various approaches to making the game }{\i\lang1033\langfe1033\langnp1033 fair -}{
\lang1033\langfe1033\langnp1033  i.e. a game in which both players can expect to have very similar scores in the long run. One method is to change Alex\rquote s coin from [1,3] to [1,}{\i\lang1033\langfe1033\langnp1033  m}{\lang1033\langfe1033\langnp1033 
] and vary the value of }{\i\lang1033\langfe1033\langnp1033 m}{\lang1033\langfe1033\langnp1033 . }{By deriving a general formula for }{\pard\plain \ql \li360\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 
\fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw740\objh340{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000020cd
83eca7c3c10103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000660000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000461700
00004d6963726f736f6674204571756174696f6e20332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020025cb2800000000000000e48f4900886d49000000000003010103010a0112834d00030f01000b01128341000011000a02822800128378000282290000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000044000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540019050000a8fdffffd80100000800190558020000
010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d01000008000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d65
73204e657720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb0220ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320a
e001cb010100000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000a706}{\result {\dn10 
{\pict{\*\picprop\shplid1042{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}
{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fReallyHidden}{\sv 0}}{\sp{\sn fScriptAnchor}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1305\pich600\picwgoal740\pichgoal340\wmetafile8\bliptag657646808\blipupi2305{\*\blipuid 2732e4d87fb678edd2a920827e13b528}010009000003e70000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002a0041200000026060f001a00ffffffff000010000000c0ffffffa6ffffff60040000c60100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a7040000002d010000
08000000320a8001d70301000000290008000000320a8001870201000000280015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000a7040000002d01010004000000f001000008000000320a8001230301000000780008000000320a80014000010000004d0015000000fb02
20ff0000000000009001010000000402001054696d6573204e657720526f6d616e0000a7040000002d01000004000000f001010008000000320ae001cb010100
000041000a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000000102022253797374656d0000040000002d01010004000000f0010000030000000000}}}}}{where Alex has coin }{\lang1033\langfe1033\langnp1033 [1,}{\i\lang1033\langfe1033\langnp1033 
m}{\lang1033\langfe1033\langnp1033 ], adapt your spreadsheet in part (11) to help improve the fairness of the game by changing the value of }{\i\lang1033\langfe1033\langnp1033 m}{\lang1033\langfe1033\langnp1033 . Test your value of }{
\i\lang1033\langfe1033\langnp1033 m }{\lang1033\langfe1033\langnp1033 on the }{\b\lang1033\langfe1033\langnp1033 100 trials + [1,m]}{\lang1033\langfe1033\langnp1033  page of the }{\field\fldedit{\*\fldinst {\lang1033\langfe1033\langnp1033 
 HYPERLINK "http://www.planetqhe.com/frames/comp2frames.html" }{\lang1033\langfe1033\langnp1033 {\*\datafield 
00d0c9ea79f9bace118c8200aa004ba90b02000000170000003100000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00650073002e00680074006d006c000000
e0c9ea79f9bace118c8200aa004ba90b6200000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00650073002e00680074006d006c000000}}}{\fldrslt 
{\field{\*\fldinst {\lang1033\langfe1033\langnp1033  HYPERLINK "http://www.planetqhe.com/frames/comp2frames.html" }{\lang1033\langfe1033\langnp1033 {\*\datafield 
00d0c9ea79f9bace118c8200aa004ba90b0200000003000000e0c9ea79f9bace118c8200aa004ba90b6200000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00
650073002e00680074006d006c000000}}}{\fldrslt {\cs17\ul\cf2\lang1033\langfe1033\langnp1033 Alex and Beth spreadsheet}}}{\lang1033\langfe1033\langnp1033 .}}}{\lang1033\langfe1033\langnp1033 
\par (13) Choose one of these methods to improve the fairness of the game.  
\par {\listtext\pard\plain\hich\af0\dbch\af0\loch\f0 (a)\tab}}\pard \ql \fi120\li720\ri0\sa120\sl-320\slmult0\widctlpar\jclisttab\tx720\aspalpha\aspnum\faauto\ls7\adjustright\rin0\lin720\itap0 {\lang1033\langfe1033\langnp1033 Fix Alex\rquote 
s coin at [1,3] but change the probability of his throwing a 3.
\par {\listtext\pard\plain\hich\af0\dbch\af0\loch\f0 (b)\tab}Fix Alex\rquote s coin at [1,3] but change his starting value.
\par }\pard \ql \li360\ri0\sa120\sl-320\slmult0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang1033\langfe1033\langnp1033 
Include in your analysis a comparison of the use of the mean and the median as measures of central tendency. You can test your fair game model on the }{\b\lang1033\langfe1033\langnp1033 100 trials + prob }{\lang1033\langfe1033\langnp1033 and }{
\b\lang1033\langfe1033\langnp1033 100 trials + start}{\lang1033\langfe1033\langnp1033  pages of the }{\field\fldedit{\*\fldinst {\lang1033\langfe1033\langnp1033  HYPERLINK "http://www.planetqhe.com/frames/comp2frames.html" }{
\lang1033\langfe1033\langnp1033 {\*\datafield 
00d0c9ea79f9bace118c8200aa004ba90b02000000170000003100000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00650073002e00680074006d006c000000
e0c9ea79f9bace118c8200aa004ba90b6200000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00650073002e00680074006d006c000000}}}{\fldrslt 
{\field\flddirty{\*\fldinst {\lang1033\langfe1033\langnp1033  HYPERLINK "http://www.planetqhe.com/frames/comp2frames.html" }{\lang1033\langfe1033\langnp1033 {\*\datafield 
00d0c9ea79f9bace118c8200aa004ba90b0200000003000000e0c9ea79f9bace118c8200aa004ba90b6200000068007400740070003a002f002f007700770077002e0070006c0061006e00650074007100680065002e0063006f006d002f006600720061006d00650073002f0063006f006d00700032006600720061006d00
650073002e00680074006d006c000000}}}{\fldrslt {\cs17\ul\cf2\lang1033\langfe1033\langnp1033 Alex and Beth spreadsheet}}}{\lang1033\langfe1033\langnp1033 .}}}{
\par }}