Joint density for bivariat random variables

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Consider the bivariate continuous distribution with pdf:
[tex]f(x,y) = 6 (1- x)^2 (1- y)^2 (1-x y)^-4 , 0 [tex]\le[/tex]x,y \le1[/tex].
(i) Show that f (x, y) is a proper pdf.
(ii) Obtain the marginal distributions of X and Y.
(iii) Test for independence of X and Y
(iv) If X and Y are not independent, find the correlation coefficient between them.