17. Consider the two-stage binomial problem wherein G, and Xi| iid Bernoulli(), i = 1,...,n. (a) Find the joint marginal distribution of

17. Consider the two-stage binomial problem wherein θ ∼ G, and Xi|θ iid

∼

Bernoulli(θ), i = 1,...,n.

(a) Find the joint marginal distribution of Xn = (X1,...,Xn).

(b) Are the components independent? In any case, describe features of the marginal distribution.

(c) Let Sn = X1 + ··· + Xn. Under what conditions does Sn have a binomial distribution? Describe features of its distribution.

(d) If dG(θ) = dθ, find the distribution of Sn and discuss its features.