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# For i = 1, . , n, let Xi be uniform on {1, 2, . , n}. Prove that the remainder of X1 + + Xn after dividing by n is uniform on {0, . , n 1}. Hint:...

For i = 1, . . . , n, let Xi be uniform on {1, 2, . . . , n}. Prove that the remainder of X1 + · · · + Xn after dividing by n is uniform on {0, . . . , n − 1}. Hint: induction.