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2. (10 points) Suppose {Xn}n20 is a DTMC, having state space S = {1, 2, 3} and tran- sition matrix P, where 1/2 1/3 1/6

2. (10 points) Suppose {Xn}n20 is a DTMC, having state space S = {1, 2, 3} and tran- sition matrix P, where 1/2 1/3 1/6 P = 0 1/3 2/3 1/2 0 1/2 (a) Suppose P(Xo = 1) = P(Xo = 2) = 1/4. Find E[X3]. (b) Find the stationary distribution 7 of this DTMC

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