pdf of product of two random variables

[wajahat]

Hi all,
When we add two random variables,their pdfs are convolved(central limit theorem) .I want to know what happens to the pdf when two random variables are multiplied.Is there any general rule like addition?

Thanking all in anticipation.

regards
wajahat

 

[AndyECE]

Summing, multiplying, and dividing uncorrelated random variables is handled in this paper. See Examples 6,7, and 8.

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1026999&isnumber=22050

 

[pangpangfish]

What about taking the log of the product and use convolution?

Hi all,
When we add two random variables,their pdfs are convolved(central limit theorem) .I want to know what happens to the pdf when two random variables are multiplied.Is there any general rule like addition?

Thanking all in anticipation.

regards
wajahat

 

[engmamj852003]

Dear guys and wajahat, kefko?

Please see this link for the multiplication of two independent gaussian random variables. I hope it can be helpful.

Wajahat: multiplication is different from addition and the convolution of the two pdf's (in the case of addition) can be easily proved.
you must read the title of Functions of several random variables and the transformation of random variables.( I read them from Alberto Leon Garcia book, the are a section in ch4 and ch 3 can help you to understand then deeply)

Best wishes;
Mohammmad

Added after 1 minutes:

sorry i forgot the link, it is:

https://mathworld.wolfram.com/NormalProductDistribution.html