Consider the Cauchy family defined in Section 3.3. This family can be extended to a location-scale family yielding pdfs of the form

The mean and variance do not exist for the Cauchy distribution. So the parameters μ and σ2 are not the mean and variance. But they do have important meaning. Show that if X is a random variable with a Cauchy distribution with parameters μ and σ, then:
(a) μ is the median of the distribution of X, that is, P(X > p) = P(X (b) μ + σ and μ - σ are the quartiles of the distribution of X, that is, P(X > μ + σ) = P(X

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f(z4, 0) = -00