Question: If a random sample of size n is selected without replacement from the finite population that consists of the integers 1, 2, . . .

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

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