If a random sample of size n is selected without replacement from the finite population that consists of the integers 1, 2, . . . , N, show that
(a) The mean of  is N + 1 / 2;
(b) The variance of  is (N + 1)(N – n) / 12n;
(c) The mean and the variance of Y = n ∙  are E(Y) = n(N + 1) / 2 and var(Y) = n(N + 1)(N – n) / 12