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5. (12 points) A Markov chain Xo, X1, X2, ... has the following transition graph: 1 1 2 D 1/2 3 D1 1/2 (a) (3pt)

5. (12 points) A Markov chain Xo, X1, X2, ... has the following transition graph: 1 1 2 D 1/2 3 D1 1/2 (a) (3pt) Provide the transition matrix for the Markov chain. (b) (3pt) Determine E[X2|Xo = x] for x {1, 2, 3}. (c) (3pt) Determine the set of stationary distributions. (d) (3pt) Is there a limiting distribution? If so, determine it. If not, explain why

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