(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) 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