[math-fun] Getting a complete set
A dumb question -- I've apparently forgotten nearly all of my probability [sigh]: Given selection-with-replacement from a set of N items, what's the formula for how many picks you need to make to have a P% probability of drawing each item at least once? /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
--- Bernie Cosell <bernie@fantasyfarm.com> wrote:
A dumb question -- I've apparently forgotten nearly all of my probability [sigh]: Given selection-with-replacement from a set of N items, what's the formula for how many picks you need to make to have a P% probability of drawing each item at least once?
/Bernie\
Let P(N,n) be the probability that in n picks each of the N items is drawn at least once. Then P(N,n) equals n! times the coefficient of t^n in [exp(t/N)-1]^N. Gene __________________________________ Do you Yahoo!? New and Improved Yahoo! Mail - Send 10MB messages! http://promotions.yahoo.com/new_mail
Gene Salamin wrote:
Let P(N,n) be the probability that in n picks each of the N items is drawn at least once. Then P(N,n) equals n! times the coefficient of t^n in [exp(t/N)-1]^N.
On a related note, suppose I have a bin of N distinct things, but I don't know N. I'm allowed to choose-with-replacement k times, and I can recognize things I've seen before, so that I can build a histogram of how many things I saw t times, for t=1,2,3,... How do I best guess N? --Michael Kleber
participants (3)
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Bernie Cosell -
Eugene Salamin -
Michael Kleber