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M4523  43d" G ~D3OG }Q% M3O& Q423 M NM44444ee??          e .&  S An`C:\My Documents\Hdnov29\Planet\images\planetcircle.JPGyK yK 4http://www.planetqhe.com/x]&`88  ]N Ab@C:\WINDOWS\Desktop\PLANET\images\blurplanet1.JPGText 2-]@]N8 c<dThere is a red warning light in case you adjust the sum of probabilities to a value other than one.<gcxx ! 6^NCC@!],!@^N9 Tt]N9 $<reset< ~v " <A ?A@?  O]J"`: ^NT Equation.3~v # <A ?A@?]J#`; _NT Equation.3%~v $ <A ?A@? O K]J$`p< <_NT Equation.3g~v % <A ?A@?'xi]J%`< x_NLT Equation.3+~v & <A ?A@? v ]J&`= _NT Equation.3O ~v ' <A ?A@?']J'`> NT Equation.3  ( \N Ab@C:\WINDOWS\Desktop\PLANET\images\blurplanet1.JPGText 2](@\N> <Use the spinners to alter the probability distribution and to alter the values of the parameters a and b. Investigate the questions on the next page.<>@  7.;$tribution and to alter the val  '@ x  MbP?_*+%MIBCR1g 3d%3 2hJX| Hd     Custom page 1XCCCustom page 2XCCCustom page 3XCC" d??U (  l  s *fS  @  <]`fSC <(1) Create a probability distribution that has P(X=4)=1. Interpret and explain the values you get for E(X) and Var(X). (2) Set b at zero and alter a. Hence find a formula for E(aX) in terms of E(X) and a. Interpret and explain your finding. (3) Set a at one and alter b. Hence find a formula for E(X+b) in terms of E(X) and b. Interpret and explain your finding. (4) Find a formula for E(aX+b) in terms of E(X), a and b (5) Set b at zero and alter a. Hence find a formula for Var(aX) in terms of Var(X) and a. Interpret and explain your finding. Find a formula for SD(aX) in terms of a and SD(X). (6) Set a at one and alter b. Hence find a formula for Var(X+b) in terms of Var(X) and b. Interpret and explain your finding. Find a formula for SD(X+b) in terms of b and SD(X). (7) Find a formula for Var(aX+b) in terms of Var(X), a and b. Find a formula for SD(aX+b) in terms of SD(X), a and b. 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