(Solved): continuous random varibles X and Y, joint distribution (joint) probability density funciton f(x,y) ...

continuous random varibles $X$ and $Y$, joint distribution (joint) probability density funciton $f(x,y)$ given as follows $f(x,y)=\{\begin{array}{l}(15/16)\left[x^{2}y+x{y}^2\right],0?x,y?2;0?x+y?2\\ 0,\text{ elsewhere }\end{array}$ a. marginal density function for each variable: $X$ and $Y$ b. Find the probability $P(0?X,Y?1;0?X+Y?1)$ c. [optional] Find the conditional probability $P(0?X?1?Y=1)$ You must first compute the conditional density function $f(x?y=1)$