Let Y have a hypergeometric distribution p(y) = r y Nr ny N n , y = 0, 1, 2,..., n. a

Chapter 3, Problem 3.216

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Let Y have a hypergeometric distribution p(y) = r y Nr ny N n , y = 0, 1, 2,..., n. a Show that P(Y = n) = p(n) = r N r 1 N 1 r 2 N 2 r n + 1 N n + 1 . b Write p(y) as p(y|r). Show that if r1 < r2, then p(y|r1) p(y|r2) > p(y + 1|r1) p(y + 1|r2) . c Apply the binomial expansion to each factor in the following equation: (1 + a)N1 (1 + a)N2 = (1 + a)N1+N2 . Now compare the coefficients of an on both sides to prove that N1 0 N2 n + N1 1 N2 n 1 ++ N1 n N2 0 = N1 + N2 n . d Using the result of part (c), conclude that n y=0 p(y) = 1. *3.217 Use the res