Let Y1 and Y2 be independent normal random variables, each with mean 0 and variance 2
Chapter 6, Problem 6.62(choose chapter or problem)
Let Y1 and Y2 be independent normal random variables, each with mean 0 and variance 2. Define U1 = Y1 + Y2 and U2 = Y1 Y2. Show that U1 and U2 are independent normal random variables, each with mean 0 and variance 22. [Hint: If (U1, U2) has a joint moment-generating function m(t1, t2), then U1 and U2 are independent if and only if m(t1, t2) = mU1 (t1)mU2 (t2).]
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer