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6. Suppose X has a standard Cauchy distribution (i.e. has a density f (x) = (7(1+ x2))- and Y = log(|X])). (a) Derive explicitly the

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6. Suppose X has a standard Cauchy distribution (i.e. has a density f (x) = (7(1+ x2))- and Y = log(|X])). (a) Derive explicitly the pdf of Y. (b) Find the moment generating function of Y. What is its domain of definition? An interesting fact from calculus is that ra-1 Jo dx = Tcosec(Ta), 0

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