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

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

Pa

(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.)

Pa

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