Let N be a hypergeometric random variable having the distribution of the number of white balls in
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Let N be a hypergeometric random variable having the distribution of the number of white balls in a random sample of size r from a set of w white and b blue balls. That is,
where we use the convention that m j
= 0 if either j m. Now, consider a compound random variable SN =N i=1Xi , where the Xi are positive integer valued random variables with αj = P{Xi = j }.
(a) With M as defined as in Section 3.7, find the distribution of M −1.
(b) Suppressing its dependence on
b, let Pw,r (k) = P{SN = k}, and derive a recursion equation for Pw,r (k).
(c) Use the recursion of
(b) to find Pw,r (2).
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