= Zn be a Poisson random variable with parameter = n. Let Yn = (Zn-n)/√n. Show t Yn converges in distribution to a standard normal random variable Z~ N(0, 1). Note t the mgf of Zn is m(t) = en(et-1) and the mgf of Z is et²/2
= Zn be a Poisson random variable with parameter = n. Let Yn = (Zn-n)/√n. Show t Yn converges in distribution to a standard normal random variable Z~ N(0, 1). Note t the mgf of Zn is m(t) = en(et-1) and the mgf of Z is et²/2
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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
Transcribed Image Text:t Zn be a Poisson random variable with parameter = n. Let Yn = (Zn-n)/√n. Show
at Yn converges in distribution to a standard normal random variable Z~ N(0,1). Note
at the mgf of Zn is m(t) = en(et-1) and the mgf of Z is et²/2.
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