The joint probability density function for two random variables X and Y is given as, fx,y...

The joint probability density function for two random variables X and Y is given as, fx,y (x, y) = (2/3)(1 + 2xy³ ), 0 < x < 1, 0 < y < 1

(a) Find the marginal probability density functions for X and Y .

(b) Are X and Y independent? Justify your answer.

(c) Show that E[X] = 4/9 and E[Y ] = 7/15 .

(d) Calculate Cov(X, Y )

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