X is proportional to Assume that the posterior for parameter (0, A) given the observation (") x+a-1 (1-x)n-0+4-1, TT (0, X) X where a and 8 depend on X. The full conditionals are binomial and beta, [0|X, A] ~ Bin(n,A), [X]X, 0]~Be(a +0,3 + n = 0); and allow for Gibbs sampling. (a) Using suggested Gibbs sampler draw 10,000 samples from the posterior (0, X). Use n = 50, a = 3, and 3 = 5. (b) The theoretical marginal posterior for [X] is beta-binomial with pdf *(0|X) = (") B(a + 6,3 + n 6), B(a, B) where B(u, v) = -1 (1-t)-1dt is standard beta function. Compare how well the histogram of 0's from (a), fits the theoretical beta-binomial density (0X).