Consider a random walk on an infinite one dimensional (d =1) lattice where the walker starts at site 1 = 0.

(a) Compute the generating functions U(2, 1) and V(z,).

(b) Compute the probability to reach site, I, during the random walk.

(c) Compute the probability that the walker reaches site != 0 and site = 1 after s = 3 and after s=4 steps. Compute the probability that the walker reaches sites / = 0 and site 1 = 1 for the first time after s = 3 and after s = 4 steps.

(d) Compute the average number of steps needed to reach site, 1 = 1, during the random walk. Explain your result.