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2. (10 pts) Consider two random variables X and Y having a joint probability density function f(x, y) = xy for 0 < y

2. (10 pts) Consider two random variables X and Y having a joint probability density function f(x, y) = xy for 0 < y < x < 2 and be zero otherwise. a) Find the marginal distributions of X and Y. b) Are X and Y independent?

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