Is $f_{XY}(x,y)$ the same as $f(x,y)$?

Question

I have a slight confusion with the notation, sometimes I find the joint density function like this: $$f_{XY}(x,y)$$ and on other occasions like this: $$f(x,y)$$ Is the same or what is the difference? Thanks!

Answer 1

In the case of $f_{XY}(x,y)$, you are specifying that the random variables you are taking the joint density of are $X$ and $Y$. If you just write $f(x,y)$, you had better be stating somewhere which random variables this joint density belongs to.