*26. Let denote the long run proportion of time a given Markov chain is in...

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*26. Let ð é denote the long run proportion of time a given Markov chain is in state /.

(a) Explain why ð,· is also the proportion of transitions that are into state

/ as well as being the proportion of transitions that are from state /.

(b) UiPij represents the proportion of transitions that satisfy what property?

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

(d) Using the preceding explain why

*j = Ó KiPij i

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