Define a sequence X₁, . . . , X_n of independent random variables such that for each k = 1, . . . , n, X_k = ±1, with probability 1/2 each. Let S = X₁ +· · · + X_n. This model describes a simple symmetric random walk that starts at the origin and moves left or right at each unit of time. Find E[S] and V[S].