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For the hierarchical model YA Poisson (A) and A~ gamma(a, 3) find the marginal distribution, mean, and variance of Y. Show that the margina distribution of Y is a negative binomial if a is an integer.

For the hierarchical model YA Poisson (A) and A~ gamma(a, 3) find the marginal distribution, mean, and variance of Y. Show that the margina distribution of Y is a negative binomial if a is an integer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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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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