Distribution for the Linear Combination of the Product of 2 Gaussians

Hi,

I am dealing with a sticky problem.
To make it simple, I'll state a "toy" version of the problem.
Suppose X1~N(0,s2) and X2~N(0,s2), where s2 ne s1
What is the distribution of A X1^2 + B X1 X2?

I know what the distribution for the product of two identical Gaussians
is, and I also know what the distribution for the product of 2
different Gaussians is, but I do not know what the distribution for
their linear combination is.

Even a pointer to a good ref would help tremendously.

TIA,

Juno

.

Relevant Pages