Question: 6.2. Consider the Markov chain {X n } whose transition matrix is where a > 0, /3 > 0, and a + /3 = 1.

6.2. Consider the Markov chain {X_n} whose transition matrix is

P = 0 0 1 2 3 0 0 0 0 B

where a > 0, /3 > 0, and a + /3 = 1. Determine the mean time to reach state 3 starting from state 0. That is, find E[TIXo = 0], where T = min{n ? 0; X = 3}.

P = 0 0 1 2 3 0 0 0 0 B 2. 0 0 3 0 0 0 1

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