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Suppose you are throwing n balls into two bins, labeled A and B. Each ball goes into bin A with probability 1/2 and bin B with probability 1/2, and the balls are thrown independently. Let NA be the total number of balls in bin A after all n balls have been thrown. (a) Let X, be the indicator random variable that equals 1 when the i'th ball falls in bin A and equals 0 otherwise. What is E[X;]? What is E[X ]? What is E[X, Xy] for i # j? (b) Compute E[NA] and E[ N ]. Hint: Write NA in terms of the indicator random variables X1, . . . ; Xn