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Math Help - Expected time from Poisson process

  1. #1
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    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!
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  2. #2
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    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.
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