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    Some questions about a Markov chain.

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    Category: Statistics > Simple Regression
    Subject: birth-death process
    Details: Let a Markov chain have transition probabilities Pi,i+1 = 1/(i+1) and Pi,0 = i/(i+1) for i=0,1,2, . . . .
    i) Is the chain positive recurrent? Or transient or null recurrent?
    ii) Does a stationary distribution exist? If it does, what is it?
    See also attachment.

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    Solution Summary

    The following outlines the process for answering several questions involving a Markov chain. Specifically, whether or not the chain is recurrent and whether or not a stationary distribution exists.