Imagine an administrator wants to hire the best secretary out of n applicants for a position. The applicants are interviewed one by one. A decision of “hired” or “rejected” must be drawn immediately after the interview. Once rejected, an applicant cannot be recalled. How should the administrator select the best candidate?
The problem here is about the optimal strategy to maximize the probability of selecting the best applicant. The answer for optimal stopping rule is to rejecting the first ~n/e applicants that are interviewed and then selecting at the first applicant who is better than ALL the applicant interviewed so far. ~n/e of applicants are viewed as the sample.
e = 2.71828, and 1/e is roughly 37%.
Benc Tan 