Buses

[davieddy]

If buses turn up regularly every half hour, and you turn up
to wait at random, then you expect to wait 15 minutes.
If they turn up on average every half hour but randomly,
what is your expected waitng time?

(this result once surprised me )

David

[Mini-Geek]

15 minutes?
No advanced formulae or anything...just a "common sense" guess.

[davieddy]

Originally Posted by Mini-Geek

15 minutes?
No advanced formulae or anything...just a "common sense" guess.

I agree that it's common sense, hence my (and most people's)
surprise at the right answer.

[wblipp]

This is impossible to answer without knowing more about the meaning of random. Any answer, from 0 to as large as you like, can be justified by the correct choices for the random processes.

Given a colloquial question by someone presumably unsophisticated in stochastic processes, I would assume that "Buses and passengers arrive according to independent Poisson processes" is the likely intention. Assuming that meaning,

it's 30 minutes. An unsophisticated explanation is that every nanosecond a biased coin is flipped, and the next bus comes when the coin flip is next heads. It doesn't matter how many times the coin has been flipped when you show up, the average time until the next head is always 30 minutes.

[davieddy]

Yes. By random I mean that the probability of the bus
turning up in the next minute is constant and independent
of how long you've been waiting.

David

[davieddy]

wblipp.
Can you shed any light on the 4 points in a plane problem?

David