Question: Problem 3: Let X and Y be two independent random variables that are both uniformly distributed on the interval [0, 1]. We then dene the

Problem 3: Let X and Y be two independent random variables that are both uniformly distributed on the interval [0, 1]. We then dene the random variable U z: X Y. 1. Compute U 's density function. For what values of p, p E R, is the expectation ]E[UP] nite? 2. Compute the joint density of (X, U). Are X and U independent? Why or why not?

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