Question: Generating a Poisson Random Variable. Let U, U,... be independent uniform (0, 1) random variables. (a) If X, (-log U.)/A, show that X, is exponentially

Generating a Poisson Random Variable. Let U, U,... be independent uniform (0, 1) random variables.

(a) If X, (-log U.)/A, show that X, is exponentially distributed with rate A.

(b) Use part

(a) to show that N is Poisson distributed with mean A when N is defined to equal that value of n such that +1 1=1 where II, U, = 1. Compare with Problem 121 of Chapter 1.

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