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Problem 1 (30 points) The random variable X and Y are independent and each is uniform in the interval (0,a). Find the probability distribution function

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Problem 1 (30 points) The random variable X and Y are independent and each is uniform in the interval (0,a). Find the probability distribution function (also known as the cumulative distribution function (CDF)) of the random variable Z=/X-Y/. Answer this question in two steps: a) First find the CDF of a function U=X-Y b) Then, answer the question (i.e., find Fz(z) with the assumption that Z=/U/

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