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!

Poisson Distribution of Accidents

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data
    In New York in the last 3 years there were 55 driving accidents. Assume all days are alike. What is the approximate probability that "in the next 3 years there will be at least 2 days with more than one accident".


    2. Relevant equations
    Poisson approximation


    3. The attempt at a solution
    P[in the next 3 years there will be at least 2 days with more than one accident]=
    1-P[in the next 3 years there will be 0 days with more than one accident]-P[in the next 3 years there will be 1 day with more than one accident]

    P[in the next 3 years there will be 0 days with more than one accident] is simple to calculate: 1095!/(1040!*1095^55), w/ 3 years=1095 days.

    But I have no idea how to calculate P[in the next 3 years there will be 1 day with more than one accident].
     
  2. jcsd
  3. Feb 5, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If you assume that the daily number of accidents is a Poisson random variable with some mean r, what is the expected number of accidents 3 years = 1095 days? Based on the only data available, how would you estimate the value of r?

    Now assuming the value of r you obtained above, what is p2 = P{>= 2 accidents in any single day}? Take it from there.

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Poisson Distribution of Accidents
  1. Poisson DIstribution (Replies: 5)

Loading...