Question

City of Ann Arbor wishes to form a Green Club, a group of people devoted to green technology. The club is open to all, and enrollment is done on rst-come- rst-serve basis. The enrollment stops when there are exactly 5 people who are born on January 1 in the club. Assume that there are always enough people in Ann Arbor who wish to join the club. Let X denote the size of the club. Find the expected value of X. (Assume that there are no leap years).

Answer 1

1820

Explanation:

X the size of the club will follow negative binomial distribution with probability of success p and number of failures r

p = 364/365, r = 5

hence E[x] = pr/(1-p) = 364/365 x 5 /(1/365) = 1820