1. Let (A1, A2, . .., Aloo) be a random permutation of the integers {1, 2, ..., 100} with all permutations equally likely. Define the random variable S 1, if A; = i Xi = 0, otherwise. (a) Determine P(X; = 1, X, = 1) for i # j. (b) Determine the variance of ET_, Xi