There is a min but no max. You can calculate a 95% or 99% confidence interval but there are possibilities where the one prisoner that turns off the light never is chosen enough to switch it off 99 times. A Long Tail.
Donna [email protected] On 2012-09-11, at 12:38 PM, Pierpaolo Bernardi <[email protected]> wrote: > On Tue, Sep 11, 2012 at 6:31 PM, Jordan Tirrell <[email protected]> > wrote: >> So after looking back at my computation, I noticed that I had forgotten a >> final step: dividing by 100. Now it looks like we're all in the 1e4 >> ballpark. >> >> My computation is pretty short to write, but it will be hard to understand >> if you aren't familiar with generating functions. >> >> G=: (1+i.99)&(*/@:((**:)%(1-99*])*1-*)) >> (*(G D. 1)) %100 >> 10423.2 >> >> Pierpaolo's estimate is incredibly close to my computation. > > 8^) > > Here's what I get with my simulation (alas, not written in J): > >> (test 100 ; number of prisoners > 10000 ; number of experiments > ) > > 10418.0462 ; average number of days > 7222.0 ; minimum number of days occurred > 14522.0 ; maximum = = = = > > > Cheers > P. > >> >> >> >> >> >> On Tue, Sep 11, 2012 at 12:09 PM, Roger Hui <[email protected]>wrote: >> >>> 100 Prisoners Simulation: Assume without loss of generality that prisoner >>> 0 is the designated "counter". A "round" is a group of selections (one per >>> day) with prisoner 0 as the fret. Thus: > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
