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  1. #1
    Member javax's Avatar
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    Determine a...

    Hello everybody.

    Given the function $\displaystyle p(x)=axe^{-\lambda x}(x\geq 0, \lambda \geq 0)$

    Determine $\displaystyle a$, such that $\displaystyle p(x)$ would be density for $\displaystyle X$
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  2. #2
    MHF Contributor matheagle's Avatar
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    You can integrate by part the density, but its a lot easier just making a substitution and recognizing the gamma function.
    OR you can recognize the mean of an exponential and you're done.
    OR recognize the gamma density.
    http://en.wikipedia.org/wiki/Gamma_distribution
    $\displaystyle \beta=\lambda$ and $\displaystyle \alpha=2$...

    $\displaystyle a=\lambda^2$
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