Question: 2. (Random walk) Let Sn = So + X1 + X2+ ... + Xn be a simple random walk, that is, So = 0 and

2. (Random walk) Let Sn = So + X1 + X2+ ... + Xn be a simple random walk, that is, So = 0 and X1, X2, ... are independent random variables such that P(Xi = 1) = p and P(Xi =-1) = 1 -p for all i 2 1. (a) Compute the distribution of Sn, that is, find the value of P(Sn = 2) for all i such that P(Sn = i) # 0. Hint: characterize the possible values that Sn can take in terms of the number of +1 or -1 steps in the random walk. Think of the distribution of the number of +1 or -1 steps

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