For a simple random walk {Xn : n = 0, 1, 2,...}, discussed

Chapter , Problem 33

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For a simple random walk {Xn : n = 0, 1, 2,...}, discussed in Examples 12.12 and 12.22, show that P (Xn = j | X0 = i) = ; n n + j i 2 < p(n+ji)/2 (1 p)(nj+i)/2 if n + j i is an even nonnegative integer for which n + j i 2 n, and it is 0 otherwise.

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