1. Let X and Y be two random variables with the same discrete uniform distributions i.e. their probability mass functions are given by P(X = k) = P(Y = k) = k 1 N' Suppose that X and Y are independent. Compute E[X + Y | X]. Hint: you may want to recall the elementary formula 2 = ke {1,2,..., N}. k(k + 1) 2

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