Question: Please show the work Problem 5.2 (10 points) Let Xo, X1, X2, ... be a Markov chain with state space S = {1, 2, 3},

Please show the work

Problem 5.2 (10 points) Let Xo, X1, X2, ... be a Markov chain with state space S = {1, 2, 3}, transition probabilities 0 1/2 1/2 P = 4/5 0 1/5 1/3 1/3 1/3 and initial distribution a"= (1/2, 0, 1/2). Find the following probabilities: (a) P[X2 = 1 | X1 = 3], (b) P[X1 = 3, X2 = 1], (c) P[X1 = 3 | X2 = 1], (d) P[Xg = 1 | X1 = 3, X4 = 1, X7 = 3]

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