Hi, I have a random variable z which is the function of three independent random variables x,y and s. How to find PDF of z from PDFs of x,y and s?

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Zoran Maksimovic

It depends on the function Z(x,y,s), and it complicates with the complexity of the function Z. Even for the sum of uniform variables it is a complicated issue. For some ideas you could start here:

https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf

and here

https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution

Askar M K

Dear Zoran Maksimovic

Thanks for inputs. here Z(x,y,s) is a non linear function. the links you mentioned will help me to get an idea to approach the problem.