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Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2,...

Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, X0 = 0, and transition probability matrix (pij ) given by   2 3 1 3 0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2   Let τ0 = min{n ≥ 1 : Xn = 0} and B = {Xτ0 = 0}. Compute P(Xτ0+2 = 2|B).

. Classify all the states of the random walk in 9-cycle.

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