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Question on exponential distribution?

  1. Feb 10, 2014 #1
    1. The problem statement, all variables and given/known data
    BR73C0s.png

    2. Relevant equations
    f(x) = eλx/x!

    3. The attempt at a solution
    Initially I thought I could solve this problem using the Law of Memoryless. That, the solution would just be P(X <= 2). However, I was wrong. Turns out the solution is P(X <= 4.5) - P(X<= 2.5). Does anyone know why?
     
    Last edited: Feb 10, 2014
  2. jcsd
  3. Feb 10, 2014 #2
    First of all the equation you listed is actually a poisson distribution. As the Poisson distribution is discrete, it really wouldn't make sense in this situation.

    http://en.wikipedia.org/wiki/Exponential_distribution

    The an exponential distribution has pdf of the form:

    f(x) = λe-λx for x ≥ 0.

    Anyway, what you said isn't quite right.

    Since this is a continuous distribution, P(X = 4.5) = 0. In fact, P(X = c) = 0 for any c.

    The solution would actually be P(X ≤ 4.5) - P(X ≤ 2.5) = F(4.5) - F(2.5).

    Where F(x) is the cumulative distribution function.

    The reason for this is that you want X to be less that 4.5, but all the stuff below 2.5 is not wanted , so you subtract off the probability that X is less that 2.5.
     
    Last edited: Feb 10, 2014
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