Question: 27. Let X be a hypergeometric random variable with probability mass function p(x) = P (X = x) = ; D x

27. Let X be a hypergeometric random variable with probability mass function p(x) = P (X = x) = ; D x <;N − D n − x < ; N n < , n ≤ min(D, N − D), x = 0, 1, 2, . . . , n. Recall that X is the number of defective items among n items drawn randomly and without replacement from a box containing D defective and N − D nondefective items. Show that Var(X) = nD(N − D) N2 * 1 − n − 1 N − 1 , . Hint: Let Ai be the event that the ith item drawn is defective. Also for i = 1, 2, . . . , n, let Xi = B 1 if Ai occurs 0 otherwise. Then X = X1 + X2 + · · · + Xn.

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