(b) Let X₁, X2,..., Xn be independent random variables and suppose that the MGF of X; is Mj(t), defined for t € Aj. Let Y = X₁ + X2+ + Xn. Show that the MGF of Y is My(t) = [];=1 Mj(t), defined for t E-1Aj. =1 (c) Use the results in (a) and (b) to find the MGF of a binomial random variable Y with parameters n and p. (d) Use the result in (d) to find the variance of a binomial random vari- able Y with parameters n and p.
(b) Let X₁, X2,..., Xn be independent random variables and suppose that the MGF of X; is Mj(t), defined for t € Aj. Let Y = X₁ + X2+ + Xn. Show that the MGF of Y is My(t) = [];=1 Mj(t), defined for t E-1Aj. =1 (c) Use the results in (a) and (b) to find the MGF of a binomial random variable Y with parameters n and p. (d) Use the result in (d) to find the variance of a binomial random vari- able Y with parameters n and p.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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