=+5. Let Yn be a finite-state, discrete-time Markov chain with transition matrix P = (pij ). If

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=+5. Let Yn be a finite-state, discrete-time Markov chain with transition matrix P = (pij ). If v is a column eigenvector for P with nonzero eigenvalue λ, then verify that Xn = λ−nvYn is a martingale, where vYn is coordinate Yn of v.

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