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I am trying to solve the following problem

In a shop on average 30 customers arrive in an hour. Assuming an exponential distribution, what is the probability that the time elapsed between two successive visits is
(i) more than 2 minutes
(ii) between 1 and 3 minutes

Is this distribution the same as a Poisson distribution where $λ=0.5$, because half a customer arrives every minute?

  • 1
    The number of customers that arrive in a specific time period has Poisson distribution. The *waiting time* between successive customer arrivals has exponential distribution.2012-06-12
  • 0
    This question is about a [Poisson process](http://en.wikipedia.org/wiki/Poisson_process) rather than a Poisson distribution2012-06-12
  • 0
    Strongly related: [Exponential distribution from Poisson](http://math.stackexchange.com/q/18894/77033)2014-03-11

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