Question: 1.5 Consider the Markov chain with state space S = {0,...,5} and transi- tion matrix 0 1 2 3 4 &5 o[.5.5000 0 1{.3.7000 0

1.5 Consider the Markov chain with state space S = {0,...,5} and transi- tion matrix 0 1 2 3 4 &5 o[.5.5000 0 1{.3.7000 0 p_2/00.10.90 3|.25.25 0 0 .25 .25 40 0.70 .3 0 5|0 2022 4 What are the communication classes? Which ones are recurrent and which are transient? Suppose the system starts in state 0. What is the probability that it will be in state 0 at some large time? Answer the same question assuming the system starts in state 5

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