If Y1 and Y2 are independent random variables, each having a normal distribution with
Chapter 5, Problem 5.143(choose chapter or problem)
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 moment-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.
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