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Poisson Process - Prob Theory

  1. Apr 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Cars pass a certain street location according to a Poisson process with rate lambda. A woman who wants to cross the street at that location wait until she can see that no cars will come by in the next T time units. Find the probability that her waiting time is T.

    2. Relevant equations

    3. The attempt at a solution
    I know that interarrival times have an exponential distribution.
    If X is the arrival of the next car,
    P(waiting time = T) = P( X > T )
    But I am not sure what this means. Any help would be appreciated.
  2. jcsd
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