4.32 (a) For the hierarchical model rain JUO BRA Land Y|A ~ 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. (b) Show that the three-stage model Y N ~ binomial(N, p), NA ~ Poisson(A), and A ~ gamma(a, B) leads to the same marginal (unconditional) distribution of Y