Re: Question: arrival-time puzzle

[Leigh Palmer <palmer@SFU.CA>]

> > Suppose a lot of busses whiz past your window.  The events are IID, that
> > is, Independent and Identically Distributed over time.  The average rate is
> > 6 busses per hour.
> >
> > Fact:  At any random time, if you ask how long it has been since the last
> > bus, the answer is 10 minutes, on average.
>
> Is this true???

Yes. It becomes obvious when one sets up the integral to calculate it.
The other part should be stated, which seems paradoxical again: the
average time 'til the *next* bus (calculated in hindsight, of course)
is also ten minutes! That, too, is obvious when one recognizes that
the second quantity can be calculated in the same manner as the first,
only on a time reversed sequence of random bus events, since the time
reversed sequence is also an IID sequence with the same average rate.

Leigh