The Jwiki essay I cited does present a proof, with some calculations involved.
Regarding the 23 vs. 24: Is it possible that it is an "index origin" problem? On Wed, Jan 18, 2012 at 6:12 AM, Linda Alvord <lindaalv...@verizon.net>wrote: > What we need is a traditional "proof", but this makes me suspicious that I > have some mistake in my strategy. I'll post what I have so far. > > Linda > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of Pablo Landherr > Sent: Wednesday, January 18, 2012 8:49 AM > To: Programming forum > Subject: Re: [Jprogramming] Challenge 4 Bountiful Birthdays > > b > [: -. [: */\@:-. [: %&365 i. NB. taking away the needless adjustment for > leap years > (0, }:b 365) -: -. ([: */ 365 %~ 365-i.)"0 i. 365 NB. comparing it to > Rogers solution in the J Wiki > 1 > 100 (6)!:2 'b 365' > 2.17831e_5 > 100 (6)!:2 '-. ([: */ 365 %~ 365-i.)"0 i. 365' > 0.00222781 > > > On Wed, Jan 18, 2012 at 2:15 PM, Pablo Landherr > <pablo.landh...@gmail.com>wrote: > > > Another solution. > > > > bdayprob > > [: -. [: */\@:-. [: %&365.25 i. > > bdayprob 24 > > 0 0.00273785 0.00819856 0.0163448 0.0271172 0.0404352 0.0561981 0.074286 > > 0.0945617 0.116872 0.141051 0.166919 0.19429 0.222967 0.25275 0.283438 > > 0.314827 0.346718 0.378912 0.411221 0.443461 0.475459 0.507053 0.538094 > > > > > > > > > > On Wed, Jan 18, 2012 at 7:03 AM, Roger Hui > <rogerhui.can...@gmail.com>wrote: > > > >> Does http://www.jsoftware.com/jwiki/Essays/Birthday%20Problem answer > any > >> of > >> your questions? > >> > >> > >> > >> On Tue, Jan 17, 2012 at 9:40 PM, Linda Alvord <lindaalv...@verizon.net > >> >wrote: > >> > >> > Capture the last row of c > >> > > >> > ]l=:{:c > >> > 106 249 7 326 308 274 81 347 276 113 108 20... > >> > > >> > And use grade up to arrange the numbers in sequence > >> > > >> > (/:l){l > >> > 0 1 3 3 4 4 5 5 6 6 7 7 7 7 8 8 8 13 13... > >> > > >> > This should be i.365 > >> > > >> > I have an idea on how to get what you want but I'll wait to see what > >> you do > >> > next. > >> > I have to use a deal without a fixed seed for the deal. > >> > > >> > I happened to remember 24 and haven't gone looking for the number and > >> > haven't the foggiest notion of how I proved it! > >> > > >> > Linda > >> > > >> > -----Original Message----- > >> > From: Linda Alvord [mailto:lindaalv...@verizon.net] > >> > Sent: Tuesday, January 17, 2012 11:25 PM > >> > To: 'Programming forum' > >> > Subject: RE: [Jprogramming] Challenge 4 Bountiful Birthdays > >> > > >> > I think we need sortleaf. > >> > > >> > Linda > >> > > >> > -----Original Message----- > >> > From: programming-boun...@jsoftware.com > >> > [mailto:programming-boun...@jsoftware.com] On Behalf Of Brian Schott > >> > Sent: Tuesday, January 17, 2012 10:14 PM > >> > To: Programming forum > >> > Subject: Re: [Jprogramming] Challenge 4 Bountiful Birthdays > >> > > >> > $c=.500 365?.@$365 > >> > $D=. i.&0"1(=&#~.)\"1 c > >> > mean D+1 NB. 25.086 > >> > pretty 5 SL sortleaf 1+D > >> > > >> > $c=. 10 500 365?.@$365 > >> > $D=. i.&0"1(=&#~.)\"1 c > >> > mean, D+1. NB. 24.6856 > >> > pretty"2] 5 SL"0 1 sortleaf"1] 1+D > >> > > >> > I am suspicious of these results because my memory is that the mean is > >> > closer to 18.5 people. Then again, other measures of the center look > >> closer > >> > to 19, just looking at the stemplots. > >> > > >> > --- > >> > (B=) > >> > > >> > On Jan 15, 2012, at 5:40 AM, "Linda Alvord" <lindaalv...@verizon.net> > >> > wrote: > >> > > >> > > > >> > > For this challenge, as usual, do not use @ but you may use > whatever > >> > style > >> > > and strategy you like to accomplish the task. > >> > > > >> > > > >> > > > >> > > The problem is to simulate the classic birthday problem. > >> > > > >> > > > >> > > > >> > > A single trial works this way. People enter a room one by one and > >> > declare > >> > > their birth date. Suppose the 29th person is the first person to > >> match a > >> > > birthday of someone in the room. The result of the first trial is > 29. > >> > > > >> > > > >> > > > >> > > Repeat for 500 trials. > >> > > > >> > > > >> > > > >> > > If you use Kip's frequency distribution of the results you have lots > >> of > >> > > information. > >> > > > >> > > > >> > > > >> > > fd=:[: /:~ ~. ,. [: +/"1 ~. =/ ] > >> > > > >> > > > >> > > > >> > > But the mean gives a more concise summary of the data. So, the > final > >> > part > >> > > of the problem is to obtain a list of 10 means of 500 trials and > >> the > >> > > mean of the means. > >> > > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
