Let (N_{i}) be the random number of time periods a discrete-time Markov chain stays in state (i)

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Let \(N_{i}\) be the random number of time periods a discrete-time Markov chain stays in state \(i\) (sojourn time of the Markov chain in state \(i\) ).

Determine \(E\left(N_{i}\right)\) and \(\operatorname{Var}\left(N_{i}\right)\).

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