(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.

Hello! As you have posted 2 different questions, we are answering the first question. In case you…

(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

(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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

(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
a particular World Cup soccer game. Thus Mike's donation is a random variable
Y = 25X + 50 where X is defined in problem 1. Find the expected value and the
variance of Y.

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