[Jprogramming] Challenge 4 Bountiful Birthdays

[Linda Alvord]

My simulations are averaging a little more than 24.  Your results seem
closer to 23. I'm interest to see what Brian will get as his strategy in the
long run is much better than mine.

I have to ponder all you work for a while but it looks like a great webpage.
I didn't think I'd be able to look at it this morning but Wiki seemed to be
awake.

Linda


-----Original Message-----
From: programming-bounces at jsoftware.com
[mailto:programming-bounces at jsoftware.com] On Behalf Of Roger Hui
Sent: Wednesday, January 18, 2012 1:03 AM
To: Programming forum
Subject: Re: [Jprogramming] Challenge 4 Bountiful Birthdays

Does http://www.jsoftware.com/jwiki/Essays/Birthday%20Problem answer any of
your questions?

u

On Tue, Jan 17, 2012 at 9:40 PM, Linda Alvord
<lindaalvord at 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:lindaalvord at 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-bounces at jsoftware.com
> [mailto:programming-bounces at 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" <lindaalvord at 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