Assume two jointly normally distributed variables X,Y.
Then what I often see is that densities are written as follows:
$f_X(x)$ as the density of X, $f_Y(y)$ as the density of Y, $f_{X,Y}(x,y)$ as the joint density, $f_{X|Y}(x|y)$ as the conditional density, and so on.
My question: Why do people include this subindex? What is the meaning behind it? Does it add any information? E.g. why don't you just write $f(x)$ or $f(X)$ instead of $f_X(x)$? Does something like $f_Y(x)$ even make sense?
Thanks a lot!