Let $X,Y$ be independent and uniformly distributed in the interval $(0,1)$. What is the joint probability density function?
The answer I get is: $$f_{X,Y}(x,y) = 1,\quad 0<x<1,\quad 0<y<1$$
Is this correct? My intuition here is completely off for some reason and I'm really confused.
Best Answer
Yes, you are correct.
$$f_{X,Y}(x,y)=f_X(x)f_Y(y)$$
since they are independent.