Question: Let Xo, X1, ... be a Markov chain whose state space is Z (the integers). Recall the Markov property: P(Xn = in | Xo =

Let Xo, X1, ... be a Markov chain whose state space is Z (the integers). Recall the Markov property: P(Xn = in | Xo = 10, X1 = i1, . . ., Xn-1 = in-1) = P(Xn = in| Xn-1 = in-1), Vn, Vit. Does the following always hold: P(Xn 20 | Xo 2 0, X1 2 0, . . ., Xn-120) = P(Xn 2 0 | Xn-120) ? (Prove if "yes", provide a counterexample if "no" )

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