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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- Jul 27th 2009, 07:17 AMdxdyProbability 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? - Jul 27th 2009, 07:39 AMmatheagle
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.