Probability density function - multivariate random variable

asked 2014-01-01 14:11:34 +0200

mresimulator
165 ●32 ●43 ●52

updated 2014-01-01 19:37:04 +0200

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.

Waiting for your answers.

Thans a lot!!

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answered 2014-01-02 08:55:31 +0200

ppurka
2111 ●17 ●38

updated 2014-01-02 21:18:11 +0200

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.

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Please see http://math.stackexchange.com/questions/624958/how-to-obtain-a-pdf-of-a-random-variable-defined-as-a-function-of-many-variables/. How can I btain this pfd using SAGE? Thanks a lot!

mresimulator ( 2014-01-02 12:17:20 +0200 )edit

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Asked: 2014-01-01 14:11:34 +0200

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Last updated: Jan 02 '14

Probability density function - multivariate random variable edit