# Expected time from Poisson process

• November 11th 2009, 05:43 PM
Artemis
Expected time from Poisson process
Hi,

Let's say I have cars passing a point as a Poisson process with having stationary flow of 100 cars/hr. How would I go about finding the expected amount of time needed to observe one headway (time between cars) larger than three times the mean headway?

Thanks!
• November 12th 2009, 07:28 AM
Focus
Arrivals in a Poisson process are $\exp(\lambda)$. Now what is the expected time between cars? Easy, $\frac{1}{\lambda}$. State your question in terms of an exponential distribution (i.e. what is the prob. that an arrival takes longer than 3 times the mean), then it should be pretty clear what the answer is.

Good luck.