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Math Help - Probability density function

  1. #1
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    Probability density function

    How can I find the probability density function of the following function of two random variables x and y
    z = 1 + ax + ax/(1 + by) + acy/(1 + by) + a^2 x^2/(1 + by)

    where x and y are chi-square random variables and a, b and c are constants?
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  2. #2
    MHF Contributor matheagle's Avatar
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    This looks like a mess. It's certainly not a linear combination, so I would try the MGF technique, but most likely that will be nasty too.

    If you want to use Jacobians, I would combine a couple of terms.
    The third and fifth terms are tough since they have both x's and y's in them.
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