Question: Xn, n = 0, 1, 2, . . ., is a simple random walk on the integers S = {. . . , 2, 1,

Xn, n = 0, 1, 2, . . ., is a simple random walk on the integers S = {. . . , 2, 1, 0, 1, 2, . . .}, starting at X0 = 0. (The probabilities of jumping left and right are 1/2.) Let T1 = min{n | Xn = 3} = the first time to get to 3. Let T = min{n > T1 | Xn = 5 or Xn = 5} = the first time after T1 to get to either 5 or -5. (a) Find ET . (20 points) (b) Find EXT . (20 points)

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