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Question 2. (15 pts) be a DTMC with state space S = {0, 1, 2, 3} and transition matrix ,... 0 1 2 3 0 1 0 0 0 1 1/2 0 0 1/2 2 1/6 1/6 1/3 1/3 3 1/6 1/3 1/6 1/3 (a) (5 pts) Identify all the communicating classes of this Markov chain. For each class, determine if it is positive recurrent, null recurrent or transient. p: (b) (5 pts) Assume X0 = 2. Find the probability that the chain will never visit state 1. (c) (5 pts) Assume X0 = 2. Find the expected time that the chain either visits state 0 or visits state 1 for the rst time