A more practical approach, IMHO, is simulation.
"Patrick D. Rockwell" wrote:
> [EMAIL PROTECTED] wrote:
> >
> > In article <[EMAIL PROTECTED]>,
> > [EMAIL PROTECTED] wrote:
> > > On Tue, 14 Dec 1999 "Patrick D. Rockwell" wrote:
> > > > Let's say that n people agree to meet between 2:00 P.M. and
> > > > 3:00 P.M... Now, what if each person is willing to wait a
> > > > different amount of time d1, d2, d3, etc,... [expressed as
> > > > fractions of an hour] What is the probability that ALL of
> > > > them meet?
> > >
> > > Obviously with n=2 the probability is simply
> > >
> > > P_2 = d1 + d2 - (d1^2 + d2^2)/2
> > >
> > > The subtractive components result from the truncation of the waiting
> > > intervals at the boundaries. It's quite a bit more work to show
> > > that with n=3 the probability, with d1 < d2 < d3, is given by
> > >
> > > P_3 = d1 d2 + d1 d3 + d2 d3
> > >
> > > - (1/2)(d1 d2^2 + d1 d3^2 + d2 d3^3)
> > >
> > > - (1/3)d1^3 - (1/6)d2^3
>
>
> Can anyone out there expand the above formula to the four person case?
> In other words
>
> p_4 = ????
>
> TIA :-)
>
> --
> Patrick D. Rockwell
> mailto:[EMAIL PROTECTED]
> mailto:[EMAIL PROTECTED]
> mailto:[EMAIL PROTECTED]
