Consider a recurrent Markov chain starting in state 0. Let m, denote the expected number of time
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Consider a recurrent Markov chain starting in state 0. Let m, denote the expected number of time periods it spends in state i before returning to 0. Use Wald's equation to show that = " j>0 m = 1. Now give a second proof that assumes the chain is positive recurrent and relates the m, to the stationary probabilities.
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