In a random walk in (0, ) with an absorbing barrier at the origin and initial position at z, let u,n(x) be the probability that the nth step takes the particle to the position x, and let (9.3) 00 Uz(s; x) = u(x)s". n=0 Using problem 19, show that U.(s; x) = V(s) -2(s) V(s). Conclude (9.4) Uzn(x) = van (q/p) Vx+2,n - Compare with the result of problem 15 and derive (9.4) from the latter by combinatorial methods.