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Homework Help: 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

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    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
     
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