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Let {??,?=0,1,2,…} be a Markov chain with the state space ?={0,1,2,3,…}. The transition probabilities are defined...

Let {??,?=0,1,2,…} be a Markov chain with the state space ?={0,1,2,3,…}. The transition probabilities are defined as follows: ?0,0=1, ??,?+1=? and ??,?−1=1−?, for ?≥1. In addition, suppose that 12<?<1. For an arbitrary state d such that ?∈?,?≠0, compute ?(??>0 ??? ??? ?≥1 |?0=?).

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