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Math Help - Exponential random variable

  1. #1
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    Exponential random variable

    Hi members,
    Show that
    $E[X^4]=[24]/[\lambda^4]$
    When X is an exponential random variable with rate $\lambda $
    Last edited by Vinod; August 17th 2014 at 02:55 AM.
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  2. #2
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    Re: Exponential random variable

    You can do this using the moment generating function.

    $M(t)=E[e^{t X}]$

    $E[X^4]=\dfrac {d^4M(t)}{{dt^4}}|_{t=0}$

    I leave the details to you.
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  3. #3
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    Re: Exponential random variable

    Or you can use the basic definition: E(X^4)= \int x^4 P(x)dx where P(x) is the probability density.
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