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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.

(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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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 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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