5. Consider a simple random walk on the set {0, 1, 2, ..., N} in which each step is to the right with probability p or to the left with probability q = 1- p. Absorbing barriers are placed at 0 and N. Show that the number X of positive steps of the walk before absorption satisfies E(X) = {Dk-k+ N(1 − Pk)} where D is the mean number of steps until absorption and pk is the probability of absorption at 0.

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