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Exercise 1 (6 + 2 + 2 pts.). Joint distribution of continuous random variables. Let U and V be independent, U N Unif((0, 1)), and V N Gamma(2,)\\). 1. Find the joint density function of (X, Y) = (UV, (1 U)V). 2. What is the marginal density of X? 3. Are X and Y independent