Question: 3. Consider a Markov chain with state space {1, 2, 3, 4, 5,6} and the following transition ma- trix: 0.2 0 0 0.8 0 0

3. Consider a Markov chain with state space {1, 2, 3, 4, 5,6} and the following transition ma- trix: 0.2 0 0 0.8 0 0 0.6 0 0 0 0.4 0 0 0.2 0.1 0.7 0 P = 0.7 0 0 0.3 0 0 0.8 0.1 0 0.1 0 0 0.9 0 0 0 0.1 (a) Find the communicating classes of the Markov chain. Which of these classes are recurrent and which are transient? (b) Find a stationary distribution 7 of this Markov chain such that 7(1) > 0 and 7 (2) = 0. (c) Find a stationary distribution 7 of this Markov chain such that 7 (1) = 0 and 7(2) > 0. (d) Find a stationary distribution 7 of this Markov chain such that 7(1) > 0 and T(2) > 0. (e) Calculate the first passage probabilities f14' and f26

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