Question 1 Let (Xn)nzo be a Markov chain with the state space S = {A, B, C, D, E, F} with the transition matrix given by P = Compute mд and mp. 000 213 12 25 13 12 0 0 0 0 0 000 0 001/0 0 0 0 0 13 12 0 0 (a) Identify the communicating classes. (b) Recall the notation for the first return time to a state and for the return probability: Ti min{n EN: Xn=i}, ie S. fi = P(Ti<∞| Xo = i), i S. Compute fA and fp. (c) Recall the notation for the expectation of the first return time: mi = E(Ti|Xo = i), iES.

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