13. You should use Matlab for solving this question. Suppose there are N + 1 spaced states located on the number line at 0, 1, 2, ..., N. The relative frequency of state i is given by the function f (i) = 2N - i. Define a proposal transition following manner: (a) If i = 0, then propose j = 0 or j = 1 with equal probability. (b) If i = N, then propose j = N or j = N - 1 with equal probability. (c) Otherwise, propose j = i + 1 with equal probability. 3 (a) Simulate a random walk on this Markov chain. Use a small / until you get the simulation working, then use N = 100. Let the random walk run for lots of steps (1,000,000 or more steps) and keep track of how many times each state is visited. (4) (b) Do you see the steady-state distribution emerge in the frequencies of visited states? You can answer this by checking that the frequencies of visiting different states at the end of your simulation steps is roughly in the same proportions as given by f (i), i = 0, ..., N. (4)