(a) For the hierarchical model

find the marginal distribution, mean, and variance of Y. Show that the marginal distribution of V is a negative binomial if a is an integer.
(b) Show that the three-stage model

leads to the same marginal (unconditional) distribution of Y.

Transcribed Image Text:

Y[A ~ Poisson(A) and A ~ gamma(a, β) YIN ~ binomial(N,P), NA ~ Poisson(A), and A ~ gamma(a, β)