This is a restatement of the puzzle I posted a few minutes ago. It's the
same idea; I just wanted to eliminate a possible source of confusion.
At 09:03 AM 7/8/00 -0400, Ludwik Kowalski wrote:
>The exponential distribution [of arrival intervals] may be counter-intuitive.
Here's an even simpler arrival-interval puzzle, which doesn't require a
Geiger counter or dice or anything else.
Part 1: Suppose busses drive past your window every ten minutes like
clockwork, all day and all night. If the last one was at 8:15 the next one
will be at 8:25, guaranteed.
Question 1a: If you start looking at a random time, how long
do you have to wait for the passage of the next bus, on average?
Question 1b: If you start looking just as one bus is passing, how
long do you have to wait for the passage of the next bus, on average?
Part 2: Same as above, except the bus passage events are random. In fact,
the events are IID (Independent and Identically Distributed over time). The
average rate is one every ten minutes, i.e. an average of 6 per
hour or 144 per day or whatever.
Question 2a: If you start looking at a random time, how long
do you have to wait for the passage of the next bus, on average?
Question 2b: If you start looking just as one bus is passing, how
long do you have to wait for the passage of the next bus, on average?
HINT: The answers to part 1 are not identical to the answers to part 2.
Final question: How do you reconcile the various answers? Never mind the
math; explain what's going on in conceptual, qualitative terms.