4. Consider the simple random walk {X,} on the set of integers Z satisfying the following. The initial state is Xo = 0 and on each step the process moves one step to the right (+1) with probability pe (0, 1) and one step to the left (-1) with probability q = 1 - p. (a) (10 pts) Prove that P(X, = i | |X,| = i, \\X2-1/= in-1, . .., |Xil = 1, |Xol = 0) = p' pit qi Obviously, i; = 1. Hint: Set j = max {k : 0