Use the Moment Generating Function (MGF) to show that the square of a standard normal random variable, Z~ N(0, 1), is a chi-squared random variable with 1 degree of freedom, Y = Z² ~ x. (Recall that the probability density function of Z N (0, 1) is f(2)=√e and the MGF of X ~ X² is Mx (t) = (1 — 2t)-¹/²).
Use the Moment Generating Function (MGF) to show that the square of a standard normal random variable, Z~ N(0, 1), is a chi-squared random variable with 1 degree of freedom, Y = Z² ~ x. (Recall that the probability density function of Z N (0, 1) is f(2)=√e and the MGF of X ~ X² is Mx (t) = (1 — 2t)-¹/²).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Use the Moment Generating Function (MGF) to show that the square of a standard
normal random variable, Z N(0, 1), is a chi-squared random variable with 1 degree of
freedom, Y = Z² ~ x². (Recall that the probability density function of Z
f(2)=e-² and the MGF of X X2 is Mx (t) = (1 – 2t)−¹/²).
N(0, 1) is
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