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Perhaps you need the algebra of random variables. By using this algebra and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from their PDF: this of course includes the standard difference and sum of random variables but also their product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.

Perhaps you need the algebra of random variables. By using this algebra and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from the PDF of their arguments: this of course includes the standard difference and sum of random variables but also their product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.

Perhaps you need the algebra of random variables. By using this algebras and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from their PDF: this of course includes the standard difference and sum of random variables but also their product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.

Perhaps you need the algebra of random variables. By using this algebra and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from their PDF: this of course includes the standard difference and sum of random variables but also their product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.

Perhaps you need the algebra of random variables. By using this algebras and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from their PDF: this of course includes the standard difference and sum of random variables but also the product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.

Perhaps you need the algebra of random variables. By using this algebras and the standard techniques of calculus you can, at least in principle, determine the PDF of functions $f(X_1, \dots, X_n)$ of $n$ random variables from their PDF: this of course includes the standard difference and sum of random variables but also their product and quotient. A now classical text is [1] which, moreover, is available at the Internet Archive (with some restrictions).

Reference

[1] Melvin Dale Springer, The algebra of random variables (English) Wiley Series in Probability and mathematical Statistics. New York etc.: John Wiley & Sons, pp. XIX+470 (1979), ISBN:0-471-01406-0, MR519342, Zbl 0399.60002.