Problem 21 Let $X$ and $y$ be two jointly continuous random variables with joint PDF $$ f_{X Y}(x, y)=\left\{\begin{array}{11} X^{2}+\frac{1}{3} y & -1 \leq x \leq 1,0 \leq y \leq 1 1 0 & \text { otherwise } \end{array} ight. $$ For $0 \leq y \leq 1$, find the following: a. The conditional PDF of $X$ given $Y=y$. b. $P(X>0 \mid Y=y) $. Does this value depend on $y$ ? c. Are $X$ and $y$ independent? SP.AS. 11821 Problem 21 Let $X$ and $y$ be two jointly continuous random variables with joint PDF $$ f_{X Y}(x, y)=\left\{\begin{array}{11} X^{2}+\frac{1}{3} y & -1 \leq x \leq 1,0 \leq y \leq 1 1 0 & \text { otherwise } \end{array} ight. $$ For $0 \leq y \leq 1$, find the following: a. The conditional PDF of $X$ given $Y=y$. b. $P(X>0 \mid Y=y) $. Does this value depend on $y$ ? c. Are $X$ and $y$ independent? SP.AS. 11821