Quote:
Originally Posted by ecriture d'adulte
The proof for the 1/e chances is based on only being able to rank candidates, B<A<C etc. If you allow more information, like one candidate is just so many standard deviations better, it ends up becoming less of a math problem with a straight solution and more of a guess on what the distribution of applicants actually looks like.
So suppose you knew that the 100 people measured came from a near infinite population that you knew was normally distributed. But you didn't know the mean or standard deviation. You then start measuring those 100 one at a time. Every time you come to a person who surpasses all the other measurements you consider stopping and predicting that he or she is the highest measurement. Based on that specific measurement and the specific measurements that came before him. What are the algorithms that:
A Calculates the chance that this particular person is indeed the possessor of the highest measurement.
B. Tells you whether this should be your pick (because the solution to question A yields a higher probability than waiting for one or more higher measurements yet.)
I'm thinking that this question has not been thought of before. If not please name it after us when you broach it to your Princeton Phd buddies.