ALL PARTS PLEASE

2. Let {Xn}ff=0 be a Markov chain with State Space S = {1,2,3, 4} and transition matrix 1/6 5/6 0 0 1/5 0 4/5 0 0 1/4 0 3/4 0 0 1/3 2/3 P: (a) Classify the states of this chain. (b) Does there exist a long run distribution ? If so, what is it ? If not, explain why not. (c) Does there exist a stationary distribution ? If so, what is it ? If not, explain why not. (d) Determine whether the chain is time reversible