57. Let p denote the proportion of all individuals who are allergic to a particular medication. An inves- tigator tests individual after individual to obtain a group of r individuals who have the allergy. Let X; = 1 if the ith individual tested has the allergy and X; = 0 otherwise (i = 1, 2, 3, . . .). Recall that in this situation, X = the number of nonaller- gic individuals tested prior to obtaining the desired group has a negative binomial distribu- tion. Use the definition of sufficiency to show that X is a sufficient statistic for p.

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