2. Markov Chain States Consider a Markov chain on the state space S = {1,2,3,4,...} with the following transition matrix: 1/2 1/2 0 0 0 2/3 0 1/3 0 0 3/4 0 0 1/4 0 P = 4/5 0 0 0 1/5 5/6 0 0 0 0 That is, Pij = i/(i + 1) if j = 1, Pij = 1/(i + 1) if j = i + 1, and Pij = 0 otherwise. (a) Classify all states of the Markov chain (transient, recurrent) (b) Determine if the Markov chain is irreducible.

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