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See question attached Problem 4. Let U be a uniform random variable on [0, 1], and let X be an independent exponential variable with mean

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Problem 4. Let U be a uniform random variable on [0, 1], and let X be an independent exponential variable with mean 1. Let M be the maximum of U and X. (a) Find the density of M. (b) What is the probability that M = X

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