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Poisson Distribution - why are these different?

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]X(t)[/itex] is a Poisson process with [itex]\lambda=0.2[/itex] events per second. What is the probability of zero events in [itex]45[/itex] seconds?

    2. The attempt at a solution

    [itex]\frac{45}{0.2}=225[/itex] ([itex]0.2[/itex] second intervals)

    so [itex]P[X=0][/itex] in [itex]225[/itex] consecutive intervals is:

    [itex]\left(e^{-0.2}\right)^{225} = 2.86 \times 10^{-20}[/itex]

    or

    [itex]\lambda = (45)(0.2)=9[/itex] events per [itex]45[/itex] seconds gives:

    [itex]e^{-9} = 1.23 \times 10^{-4}[/itex]

    Both are approx. zero, but they are way different. How come?
     
    Last edited: Apr 1, 2012
  2. jcsd
  3. Apr 1, 2012 #2

    Ray Vickson

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    Homework Helper

    The 0.2 is---as you stated originally--- the number of events per second; there is no 0.2 sec anywhere in the problem! In other words, 0.2/sec = (1/5)/sec = 1 per 5 sec. This is a good illustration of the old advice: always check your units (sec ≠ per sec).

    RGV
     
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