Consider a communications system that transmits the digits 0 and 1. Each digit transmitted must pass through

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Consider a communications system that transmits the digits 0 and 1. Each digit transmitted must pass through several stages, at each of which there is a probability p that the digit entered will be unchanged when it leaves. Letting Xn denote the digit entering the nth stage, then {Xn, n = 0, 1, . . .} is a two-state Markov chain having a transition probability matrix

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