Let X be an irreducible Markov chain and let A be a subset of the state space. Let S, and Trbe the successive times at which the chain enters A and visits A respectively. Are the sequences{Xs, r≥ 1}, {XT, r≥ 1} Markov chains? What can be said about the times at which the chainexits A?

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Answered: Let X be an irreducible Markov chain…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X be an irreducible Markov chain and let A be a subset of the state space. Let S, and Tr be the successive times at which the chain enters A and visits A respectively. Are the sequences {Xs, r≥ 1}, {XT, r≥ 1) Markov chains? What can be said about the times at which the chain : exits A?