Solution Found!
Show that the result given in Exercise 3.158 also holds for continuous random variables
Chapter 4, Problem 4.137(choose chapter or problem)
Show that the result given in Exercise 3.158 also holds for continuous random variables. That is, show that, if Y is a random variable with moment-generating function m(t) and U is given by U = aY + b, the moment-generating function of U is etbm(at). If Y has mean and variance 2, use the moment-generating function of U to derive the mean and variance of U.
Questions & Answers
QUESTION:
Show that the result given in Exercise 3.158 also holds for continuous random variables. That is, show that, if Y is a random variable with moment-generating function m(t) and U is given by U = aY + b, the moment-generating function of U is etbm(at). If Y has mean and variance 2, use the moment-generating function of U to derive the mean and variance of U.
ANSWER:Step 1 of 5
Given that,
If Y is a random variable with a moment-generating function and U is given by .