Question: 4. (15 points) Suppose {Xn}n20 is a DTMC, Whose state space is S = {1, 2, 3, 4} and whose transition matrix is P, where

4. (15 points) Suppose {Xn}n20 is a DTMC, Whose state space is S = {1, 2, 3, 4} and whose transition matrix is P, where 0.2 0 0.8 0 0 0.5 0 0.5 0.8 0 0.2 0 0 0.5 0 0.5 P: (a) Find the communicating classes of this DTMC. (b) Find the period of each state. ((2) Does this DTMC have more than one stationary distribution? Clearly explain why or Why not

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