Let $$f(x) = \left\{ \begin{array}{ll} c x^{3} y^{7} & \text{if }\ 0 \le x \le 1, \ 0 \le y \le 1 \cr 0 & \mbox{otherwise} \end{array} \right.$$ Find the following:
(a) $c$ such that $f(x,y)$ is a probability density function:
$c=$
(b) Expected values of $X$ and $Y$:
$E(X)=$
$E(Y)=$
(c) Are $X$ and $Y$ independent? (enter YES or NO)