That's correct. Giving: c=. >.(m%n)^. p%(m!n) or c=. m (% <.@^. p%!) n
if we are only interested in getting exactly n elements, then subtract the probability for at most (m-1) values from the probability of having m values: p=. -/ (m-i.2) (!*c^~%) n Marshall -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Brian Schott Sent: Friday, May 27, 2011 9:35 AM To: Programming forum Subject: Re: [Jprogramming] roll and deal Do you mean %~ instead of - / n=:4 m=:2 c=: 4 5 (m!n)*(m^c) 96 192 n^c 256 1024 (m!n)* (n-m)^c 96 192 (m!n)* (n%m)^c 96 192 (m!n)* (n%~m)^c 0.375 0.1875 (m!n)* (m%n)^c 0.375 0.1875 On Fri, May 27, 2011 at 8:05 AM, Marshall Lochbaum <[email protected]> wrote: > Provided you mean at least m distinct values, the number of ways to > have exactly m distinct values is > (m!n)*(m^c) > And the number of ways total is > n^c > Which gives us a probability of > (m!n)* (n-m)^c > > Then the answer is > c=. >.(n-m)^. p% m!n > > Marshall > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Roger Hui > Sent: Friday, May 27, 2011 2:00 AM > To: Programming forum > Subject: Re: [Jprogramming] roll and deal > > But what about the problem I posed? > >> What is the least c such that the probability of ?c$n having m >> distinct values is at least p? > > > > ----- Original Message ----- > From: Fraser Jackson <[email protected]> > Date: Thursday, May 26, 2011 22:47 > Subject: Re: [Jprogramming] roll and deal > To: Programming forum <[email protected]> > >> Hi Roger, >> >> I am sorry I somehow sent the note to Jprogramming with your name >> with lower case. >> >> I was brought up on the first edition of Feller - and we had >> calculators with crank handles to do the sums. If you want to >> incorporate any bit of it in your Essay don't hesitate. >> >> Thanks for all you are doing for J. It is just an amazing tool. >> >> Kindest regards, >> >> Fraser >> >> >> ----- Original Message ----- >> From: "Roger Hui" <[email protected]> >> To: "Programming forum" <[email protected]> >> Sent: Friday, May 27, 2011 1:24 PM >> Subject: [Jprogramming] roll and deal >> >> >> > What is the least c such that the probability of ?c$n having m >> > distinct values is at least p? >> > >> > ref: http://www.jsoftware.com/jwiki/Essays/Birthday%20Problem > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- (B=) <-----my sig Brian Schott ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
