Question: Solve................. A Markov chain with state space {0, 1, 2, 3, 4, 5; has the following transition matrix: 1/2 1/2 0 0 1/4 3/4 0

Solve.................

A Markov chain with state space {0, 1, 2, 3, 4, 5; has the following transition matrix: 1/2 1/2 0 0 1/4 3/4 0 0 P= 0 1/3 2/3 0 0 0 1/2 1/2 0 1/16 1/16 1/4 1/4 1/4 1/8 1/6 1/6 1/12 1/12 1/3 1/6] (i) Starting from state 4, find the mean time spent in state 5 before absorption. (5 marks) (ii) Starting from state 4, find the absorption probability into (2, 3). (5 marks) (iii) Starting from state 5, find the absorption probability into {0, 1}. (5 marks) [Total: 60 marks] A Markov chain with state space {0, 1, 2, 3, 4, 5} has the following transition matrix: solve (i), (ii), (iii)

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