QUESTION 4A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1.a)Prove that the characteristic function (CF) of the random variable X is Ø₂(t) = e²(eit-1).b)Use the CF in (a) to find the mean and variance of the random variable X.

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Answered: A random variable X follows a Poisson…

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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A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1. a) Prove that the characteristic function (CF) of the random variable X is Ø, (t) = e²(e¹-1). b) Use the CF in (a) to find the mean and variance of the random variable X.