- Additional Problem1 : Two random variables, $X$ and $y$, have joint probability density function given by $$ f_{X Y} (x, y)=\left\{\begin{array}{11} 4 x y & 0 \leq x \leq 1,0 \leq y \leq 1 W 0 & \text { else } \end{array} ight. $$ a) Find the joint cumulative distribution function $F_{X Y} (x, y) $ b) Find the probability of the event $X \leq \frac{1}{2}$ and $Y>\frac{1}{2}$. c) Find correlation $E[X Y]$ d) Find the covariance $\operatorname{ Cov}[X, Y]=E\left(\left(X- \mu_{X} ight)\left(Y-\mu_{Y} ight) ight]$ e) Find the correlation coefficient $ ho_{X Y}$ SP.AS. 1178