Question: 27. Let {Xn : n = 0, 1, . . .} be aMarkov chain with state space S and probability transition matrix P = (pij).

27. Let {Xn : n = 0, 1, . . .} be aMarkov chain with state space S and probability transition matrix P = (pij). Show that periodicity is a class property. That is, for i, j ∈ S, if i and j communicate with each other, then they have the same period.

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