5. Consider a finite state discrete time Markov chain {Xx} on three states S1, S2, S3 with the transition matrix P = ONHAIK (a) Find a stationary distribution 7 for P. Is it unique? (b) Is this Markov chain aperiodic? Is it irreducible? (c) Suppose that to = (P(Xo = S1), P(Xo = S2), P(Xo = S3)) = (3, 31 3) is the probability mass function at time 0. What is the probability that by time T =4 we visit state S3? (d) What is the probability that we visit state S2 or S3 by time T = 4