Pmf means probability mass function

The course is Probability Theory 2

Il. Answer the following problem. Write all necessary solutions. X and Y are jointly discrete random variables with joint PMF given by: X Y 0 1 2 Px (x) 0 0 2/15 1/15 1 3/15 6/15 0 2 3/15 0 0 Pr (y) 11. Copy and complete the table. (7 pts) 12. Compute for E(X). (2 pts) 13. Compute for E(Y). (2 pts) 14. Compute for E(XY). (3 pts) 15. Compute for Var(X). (4 pts) 16. Compute for Var(Y). (4 pts) 17. Show that the the correlation coefficient between X and Y is -0.707. (4 pts) Let X , X2, X; be random variables each having a mean u and variance o?. Further, let Cov(X, , X,) =2 , Cov(X , X,) =3 and Cov(X2, X3) =1. Define U = 2X, - X, +4X3. 18. Solve for the mean of U. (3 pts) 19. Solve for the standard deviation of U. (6 pts)