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Math Help - Question from homework

  1. #1
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    Question from homework

    Hi there,

    Phili here new to the forum can anyone help with this wuestion i have

    Find the joint probability density function of
    X+Y and X=Y where X and Y are independentexponential random variables with parameter  (landa). Show that X +Y and X=Y are independent.

    Any help would be great!

    Thanks

    Philip

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  2. #2
    MHF Contributor matheagle's Avatar
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    I assume you want X-Y and not X=Y.

    Let Z=X+Y and W=X-Y, do a 2-2 transform, jacobian and all from calc3.
    Then the new joint density should factor, giving you independence.

    Note that sums of gamma's with same second beta is a gamma.
    But I'm not sure how you're writing your exponential/gamma density.
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