PROBLEM 9* Discrete random variables $X$ and $y$ have joint PMF $$ p_X, Y}\left(x_{m}, y_{n} ight)=\left\{\begin{array} (11) 0.4, & X_(1)=-\alpha, y-(1)=2, 0.3, & x_{2}=\alpha, y_{1}=2, 0.1, & x_{2}=a, y_{2}=\alpha, 0.2, & x_{3}=1, y_{3}=1 \end{array} ight. $$ Determine the value of $\alpha$ that minimizes the correlation between $X$ and $y$, and find the minimum correlation. Are $X$ and $y$ orthogonal? (Hint: differentiate to get the minimum). SP.SD. 124