6. Implement a Metropolis algorithm to simulate the onedimensional Ising model with d = 20 spins at temperature T. That is, the target distribution is dil 1 1r(:1:) 0: exp (i Ext-n+1) , i=1 dl where a: = ($1,562, . . . ,xd) and xi = :|:1, for all 2'. Dene Mm) = Eng-=1 maxi-+1. (a) Write down the framework of your Metropolis algorithm for this problem. (b) Let T = 1. Simulate 1000 samples after 500 burnin iterations and estimate the average of Mac): E[h(m)]. (0) Repeat (b) for T = 0.1. Explain the difference in the estimated averages of h(:r:) for different T