Question: A random variable X with p.d.f. f (x) = (1/)[1/(1 + x2)] for any real x, is called a Cauchy r.v. Show that 1. this

A random variable X with p.d.f. f (x) = (1/π)[1/(1 + x2)] for any real x, is called a Cauchy r.v. Show that 1. this f is indeed a p.d.f., 2. E(X) does not exist, because the integral of x f (x) is not absolutely convergent.

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