(a) Recall that for a random variable X and constants a and b, E(aX+b) = aE(X) +b.Prove thatVar(aX + b)== a²Var(X).(b) Mike agrees to donate 50 dollars to charity, plus 25 dollars for every goal scored ina particular World Cup soccer game. Thus Mike's donation is a random variableY = 25X + 50 where X is defined in problem 1. Find the expected value and thevariance of Y.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99
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(a) Recall that for a random variable X and constants a and b, E(aX+b) = aE(X) +b. Prove that Var(aX+b) = a²Var(X). (b) Mike agrees to donate 50 dollars to charity, plus 25 dollars for every goal scored in