# Probability density function - multivariate random variable

Hi experts!

I know that many of you are professional mathematicians. My question is about statcistics and sage:

given two independient random variables X and Y (with a probability density function fX and fY), and the multivariable random variable A defined by: A=h(X,Y),

How can I obtain the explicit equation of probability density function of random varible A?

I only know that the join probability density fuction fXY is fXY=fX*fY (because there are independent).

Like you can see in the article http://en.wikipedia.org/wiki/Probabil... section 'Multiple variables' we can write the pdf of A using Dirac delta function.

Thans a lot!!

edit retag close merge delete

Sort by ยป oldest newest most voted

This question should go into math stack exchange. The formula/transformation you are looking for is the one with the Jacobian, not the one with the Dirac Delta function.

For two variables, you can define another function Z = g(X,Y) which along with W = h(X,Y) is bijective and differentiable (as explained in Wikipedia). Then the Jacobian will work and you can later integrate over Z to get W.

In terms of computing it, I am not aware of anything which can easily compute these distributions/densities. You are probably better off deriving it mathematically. Alternatively, look into whether R can do this.

more