*41. Consider a Markov chain with states equal to the nonnegative integers, and suppose its transition probabilities...

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*41. Consider a Markov chain with states equal to the nonnegative integers, and suppose its transition probabilities satisfyI mage.

AssumeI mage, and letI mage be the probability that the Markov chain is ever in state j. (Note that becauseI mage.) Argue that forI mage IfI mage, findI mage forI mage.

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