Definition of Support I am a bit confused with the definition regarding support. Say the joint density function exists. For the random variables $X$ and $Y$, is the joint support of $X$ and $Y$:
the values $X$ and $Y$ can take st. $f_{X,Y}(x,y) >0$?
Or is the support of $f_{X,Y}(x,y)$ the values $X$ and $Y$ can take st. $f_{X,Y}(x,y) >0$
In other words is it defined in terms of Random variables or probability density functions? Or are they both correct?

it is defined in terms of the random variables.
AS the OP just edited , hence support is defined in terms of the random variable when joint probability density function exists.
