# What is the joint probability density function of two independent uniformly distributed random variables between (0,1)?

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

Is this correct? My intuition here is completely off for some reason and I'm really confused.

$$f_{X,Y}(x,y)=f_X(x)f_Y(y)$$