57. Let p denote the proportion of all individuals who are allergic to a particular medication. An investigator tests individual after individual to obtain a group of r individuals who have the allergy. Let Xi  1 if the ith individual tested has the allergy and Xi0 otherwise

(i  1, 2, 3, . . .). Recall that in this situation, X  the number of nonallergic individuals tested prior to obtaining the desired group has a negative binomial distribution. Use the de nition of suf ciency to show that X is a suf cient statistic for p.