Let , denote the long-run proportion of time a given Markov chain is in state i. (a)

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Let , denote the long-run proportion of time a given Markov chain is in state i.

(a) Explain why, is also the proportion of transitions that are into state i as well as being the proportion of transitions that are from state i. (b),P represents the proportion of transitions that satisfy what property?

(c) P represent the proportion of transitions that satisfy what property?

(d) Using the preceding explain why

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