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Math Help - Random Variables, Density function

  1. #1
    Junior Member
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    Random Variables, Density function

    I have no idea how to approach the following problem:

    Random Variable X has density function

    f(x) = \left\{ \begin{array}{ll}<br />
ke^{-hx}, & x \geq 0 \\<br />
0 & x<0 \end{array} \right.

    Find the value of k and determine E(x).
    Last edited by mr fantastic; July 2nd 2009 at 10:07 PM. Reason: Fixed latex (exponents require ^{} not ^() ) and formatted pdf as an array
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  2. #2
    Super Member Random Variable's Avatar
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     f(x) = ke^{\text{-}hx} for  x \ge 0


    so  k \int_{0}^{\infty} e^{-hx} \ dx = 1

    and after you find k (which is in terms of h)

     E(X) = k \int^{\infty}_{0} xe^{-hx} \ dx
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  3. #3
    MHF Contributor matheagle's Avatar
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    This is an exponential density, which is a gamma with \alpha=1 and \beta=h.
    http://en.wikipedia.org/wiki/Exponential_distribution
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