45. Consider an irreducible finite Markov chain with states 0, 1, . . . ,N. (a) Starting...

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45. Consider an irreducible finite Markov chain with states 0, 1, . . . ,N.

(a) Starting in state i, what is the probability the process will ever visit state j?

Explain!

(b) Let xi = P{visit state N before state 0|start in i}. Compute a set of linear equations that the xi satisfy, i = 0, 1, . . . ,N.

(c) If

jjPij = i for i = 1, . . . ,N − 1, show that xi = i/N is a solution to the equations in part (b).

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Introduction To Probability Models

ISBN: 9780123756862

10th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 16, 2024 04:01 AM

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45. Consider an irreducible finite Markov chain with states 0, 1, . . . ,N. (a) Starting...

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Introduction To Probability Models

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