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).

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Mathematics

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12 November, 16:57

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).

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Desmond · Answer 1

1820

Step-by-step 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