1. Let X?, be a Markov chain with the state space {1,2,3} and transition matrix 1/2 1/2 0 1/3 1/3 1/3 P = (a) Calculate the stationary distribution for X?. (b) What is the long run proportion of time X, spends in state 1 if it starts in state 2? (c) What is the expected return time to state 1 if Xo = 1?

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