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(a) For the hierarchical model YA Poisson (A) and 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. (b) Show that the three-stage model YIN 2 binomial (N, p), NA~ Poisson(A), and leads to the same marginal (unconditional) distribution of Y. A gamma(a, B) 2 gamma(a, 3)

(a) For the hierarchical model YA Poisson (A) and 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. (b) Show that the three-stage model YIN 2 binomial (N, p), NA~ Poisson(A), and leads to the same marginal (unconditional) distribution of Y. A gamma(a, B) 2 gamma(a, 3)

MATLAB: An Introduction with Applications
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 2 A gamma(a, B) 2 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. (b) Show that the three-stage model YIN binomial(N, p), NA~ Poisson(A), and leads to the same marginal (unconditional) distribution of Y. gamma(a, 3)
Transcribed Image Text:(a) For the hierarchical model YA Poisson (A) and 2 A gamma(a, B) 2 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. (b) Show that the three-stage model YIN binomial(N, p), NA~ Poisson(A), and leads to the same marginal (unconditional) distribution of Y. gamma(a, 3)
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