1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability/Poisson Problem

  1. Apr 20, 2008 #1
    Suppose that cars travelling at night on a freeway arrive at a toll station according to a Poisson process with rate alpha @=5 per minute. If five cars arrived in [0,3] (that is, during a three minute period starting at midnight), what is the conditional pmf of the number of cars that arrived in [0,1] (during the first minute of the period)?
     
  2. jcsd
  3. Apr 22, 2008 #2
    Welcome to PF

    What do you mean by pmf? Probability mass function?

    Anyways, You condition on the even that up t=3 five cars arrived. what do you know about the conditional distribution of the arrival times of these five cars?

    Hint: It's a famous property of the Poisson process because of which it is sometimes referred to as the "most random" point process of all.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?