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The probability density function of a bivariate random variable (X,Y) is given by f(x,y) = 2xy, 0 < y < x < 1, 0 otherwise. Find (i) the marginal probability density functions f(x) and f(y), (ii) the conditional density functions f(x|y) and f(y|x), (iii) E(X) and E(Y), and (iv) Are X and Y independent?
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