(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…

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) For the hierarchical model YA Poisson (A) and A~ gamma(a, 3) 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. ~