Question: 32. For a simple random walk {Xn : n = 0,1,2, . . .}, discussed in Examples 12.12 and 12.21, show that if n +

32. For a simple random walk {Xn : n = 0,±1,±2, . . .}, discussed in Examples 12.12 and 12.21, show that

P(X = j | Xoi) = n n+j-ip(n+j-i)/(1 - p)(n-j+i)/2 2

if n + j − i is an even nonnegative integer for which

image text in transcribed

and it is 0 otherwise.

P(X = j | Xoi) = n n+j-ip(n+j-i)/(1 - p)(n-j+i)/2 2

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