Question 4 (10 points) Let (X,Y) be jointly bivariate normal with x=0,x2=1,y=1,y2=4 and =21. - Show the variance-covariance matrix. - Find P(X+Y>0) MS325 October 29, 2022 - Find the constant a such that aX+Y and X+2Y are independent. [Hint: zero correlation impiles independent for normal.] - Find P(X+Y>02XY=0). [Hint: let U=X+Y,V=2XY, so (U,V) are jointly normal, find their mean, variance, covariance. Then you can calculate the conditional probability.] Question 4 (10 points) Let (X,Y) be jointly bivariate normal with x=0,x2=1,y=1,y2=4 and =21. - Show the variance-covariance matrix. - Find P(X+Y>0) MS325 October 29, 2022 - Find the constant a such that aX+Y and X+2Y are independent. [Hint: zero correlation impiles independent for normal.] - Find P(X+Y>02XY=0). [Hint: let U=X+Y,V=2XY, so (U,V) are jointly normal, find their mean, variance, covariance. Then you can calculate the conditional probability.]