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Math Help - Exponetial distribution problem

  1. #1
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    Exponetial distribution problem

    Can anyone help me solve this - I get negative values...

    When I go swimming, the distance in meters that I can swim before getting cramp in one of my hands is exponentially distributed with mean 332.4 meters. What is the probability that, on a random occasion when I go swimming, I swim a total of at most 493.1 meters without getting hand cramp given that I swim at least 324.5 meters without getting cramp?

    Thanks, F
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  2. #2
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    Re: Exponetial distribution problem

    Could you show your work?
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  3. #3
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    Re: Exponetial distribution problem

    Now i just get zero for all my probabilities:

    Can you confirm that the question is asking:


    P(x=493.1| 324.5<X<493.1) because to not get cramp would mean swimming the longest distance before getting it?

    However, when I use these big numbers in the standard exp dist functions of:
    letting lamda = 332.4, a = 324.5, b = 493.1 and z = 493.1

    ( exp (-lamda*z)-exp(-lamda*a) ) / ( exp (-lamda*b)-exp(-lamda*a))

    Which would cancel (must mean I'm wrong somewhere). But even putting in exp(-163906) it always zeros?!?
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  4. #4
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    Re: Exponetial distribution problem

    First, E[X]=\frac{1}{\lambda}=332.4, so \lambda=\frac{1}{332.4}.

    Second, exponential distribution is continuous, so the probability that X equals any concrete real number is zero.

    Can you confirm that the question is asking:

    P(x=493.1| 324.5<X<493.1)
    I think that "swim a total of at most 493.1 meters" means X\le493.1 and "swim at least 324.5 meters" means X\ge324.5. So, the question is to find \mbox{Pr}(X\le493.1\mid X\ge324.5)=1-\mbox{Pr}(X>493.1\mid X>324.5). Now you can use the memorylessness property of the exponential distribution.
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