Consider a random walk in one dimension for which the walker at each step is equally likely to take a step with displacement anywhere in the interval d-a<=x<=d+A where a < d Each step is independent of the others. After N steps the walker's displacement is S = X++XN, where X, is the displacement during the ith step. After N steps,

(a) what is the average displacement, (S), and

(b) what is his standard deviation?