20. The joint density of X and Y is given by $$f(x, y) = begin{cases} xe^{-(x+y)} &text{x...
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20. The joint density of X and Y is given by
$$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}
$$
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