X and Y have joint density function fx(x,y)=B(1+xy), \x{<1,[y{1; zero, otherwise. (1) Find B so that fx(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? and Y2 are independent.
