Question: 5. Suppose that {X},is Markov chain with transition probability matrix P = (py) and state space {1, 2, 3, ...}. Suppose that state 1 is

5. Suppose that {X},is Markov chain with transition probability matrix P

5. Suppose that {X},is Markov chain with transition probability matrix P = (py) and state space {1, 2, 3, ...}. Suppose that state 1 is recurrent and that states 1 and 2 communicate. Prove carefully or disprove via a counterexample that State 2 is recurrent

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