6. The joint density function of X and Y is $$f(x,y) = begin{cases} xy & 0 <...
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6. The joint density function of X and Y is
$$f(x,y) =
\begin{cases}
xy & 0 < x < 1, 0 < y < 2 \\
0 & \text{otherwise}
\end{cases}$$
(a) Are X and Y independent?
(b) Find the density function of X.
(c) Find the density function of Y.
(d) Find the joint distribution function.
(e) Find E[Y].
(f) Find P(X + Y < 1).
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