Let X, Y ~ N(0, 1) be independent. Find the moment generating function of X2 + Y2. Hint: If X, Y are indepenent, then X2 and Y2 are independent.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Let X, Y ~ N(0, 1) be independent. Find the moment generating function of X2 + Y2.

Hint: If X, Y are indepenent, then X2 and Y2 are independent.
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