# Thread: how to prove this pdf relation?

1. ## how to prove this pdf relation?

Given iid continuous random variables $X_1, X_2,...,X_n$, let $Y=g(X_1,...,X_n)$ be some well-behaved function (e.g., sum) of these r.v.'s and $f$ be the joint pdf of $X_1, ...,X_n,Y$. Do we have $f(x_1,...,x_n,y)=f(x_1,...,x_n)$ if $y=g(x_1,...,x_n)$ and $f(x_1,...,x_n,y)=0$ if $y\neq(x_1,...,x_n)$? If so, how to prove? This statement is obviously true for pmf, but I have no idea for pdf.
Thanks a lot!