Answer the following:

2. Implement a Metropolis algorithm to simulate the one-dimensional Ising model with d = 20 spins. That is, the target distribution is 7(a) x exp d-1 _ Militi , where a = (X1, X2, . .., a) and x; = 11, for all i. Define h(ac) = - d- 1 Cili+1 . (a) Write down the framework of your Metropolis algorithm for this problem. (b) Let T = 1. Simulate 1000 samples after 500 burn-in iterations and estimate the average of h(ac): En[h(ac)]. (c) Repeat (b) for T = 0.1. Explain the difference in the estimated averages of h(a) for different T