\begin{equation*} f(x,y) = \begin{cases} 1, & 0 \le x \le 1, 0 \le y \le 1\\ 0, & \text{elsewhere} \end{cases} \end{equation*} Give a solution for each of the following worth 5 points each. Solve without integration.\\ a. Find the marginal densities for X and Y.\\ b. What is P(0.3<X<0.5)? What is P(0.3<Y<0.5)?\\ c. For what values of Y is the conditional density f(x|y) defined?\\ d. For any y, 0 ? y ? 1, what is the conditional density function of X given that Y=y?\\ e. Find P(0.3<X<0.5|Y=0.3).\\ f. Find P(0.3<X<0.5|Y=0.5).\\ g. Given an intuitive explanation why the answer to parts e and f are the same.