Let (Xn)nzo be a Markov chain with state space S = {A, B, C, D, E, F, G, K} and transition matrix P given by P = 1 00 [0 00 10 1 0 00 1 100 6 0 00 0 000/ 00 00 0000 100000-000 TOOLTISO (b) Explain why G is a recurrent state. 00 01 0 0 0 00 0 0 0 111 0 10 OOOOO 1 00 03/3 0 3 31010 WIT 2 (a) Compute E(VE|Xo = D), the expected number of visits to state to E by the chain starting at D. (c) Suppose that the chain starts at D. Compute the probability that G is the first recurrent state that the chain hits. (d) Does the chain has a stationary distribution? Justify your answer.

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