Consider the Markov chain (Xn)nzo with state space S = {0, 1, 2, 3} and transition probability matrix 1 0 8 17 0 0 5 17 0 P = 4 17 0 8 11 29 29 0 0 Define by T the time the process first reaches one of the absorbing states 0 and 3. Compute the following: 10 29 0 1 (a) the probabilities of absorption: P(XT = 0 | Xo = 1) = P(XT = 0 | Xo= 2) = P(XT = 3 | Xo = 1) = P(XT = 3 | Xo = 2) = (b) the expected time until absorption: E[T|Xo = 1] = E[T|Xo = 2] =

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