(a) For the hierarchical modelYA Poisson (A) and2A gamma(a, B)2find the marginal distribution, mean, and variance of Y. Show that the marginaldistribution of Y is a negative binomial if a is an integer.(b) Show that the three-stage modelYIN binomial(N, p), NA~ Poisson(A), andleads to the same marginal (unconditional) distribution of Y.gamma(a, 3)

As per bartleby guidelines we can solve only first question and rest can be reposted

Answered: (a) For the hierarchical model YA…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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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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(a) For the hierarchical model YA Poisson (A) and A gamma(a, B) find the marginal distribution, mean, and variance of Y. Show that the marginal distribution of Y is a negative binomial if a is an integer.