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Statistics - Poisson distribution question.

  1. Apr 29, 2013 #1
    Hi,
    1. The problem statement, all variables and given/known data
    I am somewhat perplexed by the proposed solution to the following Statistics problem and was hoping one of you might be willing to help me settle this:
    An operator receives phone calls between 8AM and 4PM at an average rate of 20 calls/hour. No call was received during the first 3 minutes. What is the probability that we shall have to wait at least one more minute before the first call is received?


    2. Relevant equations



    3. The attempt at a solution
    Now, the book states it ought to be P(T≥1) = 1 - FT(1) = e-1/3.
    My question is, why should it not have been 1 - [F(4) - F(3)], i.e. the complement of a call received between the 3rd and 4th minutes?
    I'd appreciate it if any of you could explain this to me.
     
  2. jcsd
  3. Apr 29, 2013 #2

    Ray Vickson

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    Homework Helper

    If T is the time of the first arrival, you want P{T > 4 | T > 3}, because you are told that the event {T > 3} occurred.
     
  4. Apr 29, 2013 #3
    Thank you, Ray! It's clearer now :-).
     
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