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pdf of product of two dependent rv

Started by sair...@gmail.com August 24, 2006
Hello,
                I am facing problem in finding the pdf of  Z= AB+CD,
where A, B, C, D are  independent normal random variables  with zero
mean and uneqaul variances.
I could bale to find out the pdf's of each term (i.e. AB or CD).  It is
a well known result that AB has a pdf of   modified Bessel function of
the second kind.
 If we add two random variables having the pdf of " modified Bessel
function of the second kind.", assuming both are independent, I am
unable to get the final expression . Since it involves the convolution
of two " modified Bessel function of the second kind.".
Is there any standard expression for finding the pdf of
z= AB+CD?
Best Regards,
-SaiRamesh.

sairamesh@gmail.com wrote:
> Hello, > I am facing problem in finding the pdf of Z= AB+CD, > where A, B, C, D are independent normal random variables with zero > mean and uneqaul variances. > I could bale to find out the pdf's of each term (i.e. AB or CD). It is > a well known result that AB has a pdf of modified Bessel function of > the second kind. > If we add two random variables having the pdf of " modified Bessel > function of the second kind.", assuming both are independent, I am > unable to get the final expression . Since it involves the convolution > of two " modified Bessel function of the second kind.". > Is there any standard expression for finding the pdf of > z= AB+CD? > Best Regards, > -SaiRamesh.
I think you can numerically obtain the pdf of z (by plotting in matlab) but I do not think any analytical result can be obtained by convolving 2 Bessel functions