(a) For the hierarchy in Example 4.4.6, show that the marginal distribution of X is given by...

Question:

(a) For the hierarchy in Example 4.4.6, show that the marginal distribution of X is given by the beta-binomial distribution,

(b) A variation on the hierarchical model in part (a) is

X|P ~ negative binomial(r, P) and P ~ beta(α, β).

Find the marginal pmf of X and its mean and variance. (This distribution is the beta-Pascal.)

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...