the mean and variance of a random variable X that has a discrete uniform distribution on the n integers a, a + 1, a + 2, ..., b, i.e. b = a + n -1, is given by: at b H = E(X} 2 02 = V{X} = E((X - M)3} = - (b - a +1)2 - 1 12 Use the identities 1 + 2 + 3 + + n = n (n + 1) / 2 and 1 + 22 + 32 + .. + n? = n (n + 1)(2n + 1) / 6 to derive the above formulas