94. 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 thatI mage if eitherI mage orI mage. Now, consider a compound random variableI mage, where the are positive integer valued random variables withI mage.

(a) With M as defined as in Section 3.7, find the distribution of .

(b) Suppressing its dependence on

b, let Image, and derive a recursion equation for Image.

(c) Use the recursion of

(b) to find .