Question: Exercise 1 (6 + 2 + 2 points.). Joint distribution of continuous random variables. Let U and V be independent, U N Unif((0,1))1 and V

Exercise 1 (6 + 2 + 2 points.). Joint distribution of continuous random variables. Let U and V be independent, U N Unif((0,1))1 and V N Gamma(21)\\). 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

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