(a) A hen lays N eggs where N is Poisson with parameter λ. The weight of the nth egg isWn, where W₁, W2,... are independent identically distributed variables with common probabilitygenerating function G(s). Show that the generating function Gw of the total weight W = Σ₁ Wiis given by Gw (s) = exp{-λ + AG (s)}. W is said to have a compound Poisson distribution. Showfurther that, for any positive integral value of n, Gw (s)1/n is the probability generating function ofsome random variable; W (or its distribution) is said to be infinitely divisible in this regard.(b) Show that if H (s) is the probability generating function of some infinitely divisible distributionon the non-negative integers then H(s) = exp{-λ + AG (s)} for some λ (> 0) and some probabilitygenerating function G(s).

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Answered: (a) A hen lays N eggs where N is…

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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