1. Problem 12.3 Suppose that the probability density function f (x, y) of the random variables X and Y is given by the bivariate standard normal density with parameter ρ. Verify that the probability density function fZ(z) of the ratio Z = X/Y isgiven by the so-called Cauchy density

∞

−∞

|y| f (zy, y)dy = (1/π)

1 −ρ2

(z −ρ)2 +1−ρ2

,

(a−μ1)/σ1

−∞