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Math Help - Probability density function

  1. #1
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    Exclamation Probability density function

    Can someone help me with this question.
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  2. #2
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    Quote Originally Posted by Freemymind View Post
    Can someone help me with this question.
    a. Where are you stuck with doing the integration?

    b. \mu = E(X) = \int_0^{+ \infty} x a e^{-ax} \, dx. Do this integral using integration by parts. Show your working and where you get stuck if you can't do it.

    Let the median be m. Solve \int_0^{m}a e^{-ax} \, dx = \frac{1}{2} for m. Show your working and where you get stuck if you can't do this.
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  3. #3
    MHF Contributor matheagle's Avatar
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    In case you're interested this is an exponential random variable, which is a subset of the gamma family.
    Also the parameter a needs to be positive, it does have to be in the interval (0,1).
    You can check your answer at http://en.wikipedia.org/wiki/Exponential_distribution
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  4. #4
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    For a I got

    -e^(-a(b))- (-e^(a(0)) b = infiniti

    But that does not give me 1
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  5. #5
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Freemymind View Post
    For a I got

    -e^(-a(b))- (-e^(a(0)) b = infiniti

    But that does not give me 1

    I have no idea what this means and e^0=1.
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