Question: Let X be a Markov chain with M states. - Prove that if state j can be reached from state i , then it can

Let X be a Markov chain with M states.

- Prove that if state j can be reached from state i, then it can be reached in M steps or less.

-Let P be the transition probability matrix of the Markov chain X. Argue that if for some positive integer r, Pr has all positive entries, then so does Pn, for all integers nr .

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