20. The joint density of X and Y is given by

$$f(x, y) =

\begin{cases}

xe^{-(x+y)} &\text{x > 0, y > 0} \\

0 &\text{otherwise}

\end{cases}

$$

Are X and Y independent? What if f(x, y) were given by

$$f(x, y) =

\begin{cases}

2 &\text{0 < x < y, 0 < y < 1} \\

0 &\text{otherwise}

\end{cases}

$$