Consider the Markov chain (Xn)n20 with state space S = {0, 1, 2} and transition probability matrix 10 12 23 23 P = 9 9 19 19 0 0 Define by T the time the process first reaches the absorbing state 2. Compute the following: 1 23 1 19 1 (a) the expected times until absorption E[T|Xo = 0] = E[T| Xo = 1] = (c) the probability P(T≥ 3) = (b) the probabilities P(T> 2 | Xo = 0) = P(T> 2 | Xo = 1) = given that P(Xo = 0) = 0.2 and P(Xo = 1) = 0.8.

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A: It is an important part of statistics. It is widely used.

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