Let the joint distribution of X and Y be given in the table below:
Y
1 2 3 4
X 1 0.12 0.21 0.24 0.03
2 0.06 0.06 0.12 0.06
3 0.02 0.03 0.04 0.01
(a) Find the marginal distributions of X and Y.
(b) Are X and Y independent?
(c) Find E(X), E(Y ), E(4X - 2Y ).
(d) Find E(XY ), Cov(XY ) and Var(X - 3Y ).