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If Y1 and Y2 are independent random variables, each having
Chapter 5, Problem 143E(choose chapter or problem)
Problem 143E
If Y1 and Y2 are independent random variables, each having a normal distribution with mean 0 and variance 1, find the moment-generating function of U = Y1Y2. Use this ment-generating function to find E(U ) and V (U ). Check the result by evaluating E(U ) and V (U ) directly from the density functions for Y1 and Y2.
Questions & Answers
QUESTION:
Problem 143E
If Y1 and Y2 are independent random variables, each having a normal distribution with mean 0 and variance 1, find the moment-generating function of U = Y1Y2. Use this ment-generating function to find E(U ) and V (U ). Check the result by evaluating E(U ) and V (U ) directly from the density functions for Y1 and Y2.
ANSWER:
Solution:
Step 1 of 3:
It is given that the independent random variables and are Normally distributed with mean 0 and variance 1. A variable U is defined as U=.
We have to find the moment generating function of U.Also we have to find the mean and variance of U using the moment generating function and the direct method.