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Let X,, X2, ..., X, be i.i.d. standard normal random variables, i.e., with mean 0 and variance 1, and let Y; = X? for all i = 1, ..., n. Find the moment generating function of Y, to show that Y; ~ x²(1)

Let X,, X2, ..., X, be i.i.d. standard normal random variables, i.e., with mean 0 and variance 1, and let Y; = X? for all i = 1, ..., n. Find the moment generating function of Y, to show that Y; ~ x²(1)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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Let X, X2, ... , X, be i.i.d. standard normal random variables, i.e., with mean 0 and variance 1, and let Y, = X? for all i = 1, ... , n. Find the moment generating function of Y, to show that Y; ~ x²(1)
Transcribed Image Text:Let X, X2, ... , X, be i.i.d. standard normal random variables, i.e., with mean 0 and variance 1, and let Y, = X? for all i = 1, ... , n. Find the moment generating function of Y, to show that Y; ~ x²(1)
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