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Problem 5. (10 pts) Let X be a continuous Cauchy random variable with the cumulative distribution function F(:r) z iarctantr) + %. Suppose that Y

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Problem 5. (10 pts) Let X be a continuous Cauchy random variable with the cumulative distribution function F(:r) z iarctantr) + %. Suppose that Y is a uniform random variable on [$1] and Y is independent of X. Compute the density function of the random variable F (X ) + 21"

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