Consider a hierarchical Bayes model with Exp(1), i | i.i.d. Gamma(k, ), i = 1, 2, . . . , n and yij | , i i.i.d. P oisson(i), i = 1, . . . , n, j = 1, . . . , m, where is a rate parameter, and k, n, m are fixed and known. a. Write down the posterior distribution 1, . . . , n, | yij , i = 1, . . . , n, j = 1, . . . , m b. Find full conditional distributions, and give details of one full iteration of the Gibbs sampler to draw from the above posterior distribution