Write all your steps leading to the answers.) X and Y have joint density function f_(XY)(x,y)=B(1+xy), |x|<1,|y|l; zero, otherwise.
(1) Find B so that f_(XY) (x,y) is a valid joint density function.
(2) Prove or disprove X, Y are uncorrected.
(3) Prove or disprove X, Y are independent.
(4) Prove or disprove X^2 and Y^2 are independent.
