(Solved): Two random variables, X and Y, have joint probability density function given by fXY(x,y)={4xy0 ...

Two random variables, $$X$$ and $$Y$$, have joint probability density function given by $$f_{XY}(x,y)=\{\begin{array}{ll}4xy& 0?x?1,0?y?1\\ 0& \text{ else }\end{array}$$ a) Find the joint cumulative distribution function $$F_{XY}(x,y)$$ b) Find the probability of the event $$X?\frac{1}{2}$$ and $$Y>\frac{1}{2}$$. c) Find correlation $$E[XY]$$. d) Find the covariance $$\mathrm{Cov}[X,Y]=E{\left[\left(X?{?}_X\right)\left(Y?{?}_Y\right)\right]}_{\text{, }}$$, e) Find the correlation coefficient $${?}_{XY}$$