Let \(X\) and \(Y\) have joint density \[ f(x,y)=g\left (\sqrt {x^2+y^2}\right ),\qquad (x,y)\in \mathbb {R}^2, \] for some function \(g\). Show that \(Z=X/Y\) has a Cauchy density.
Question
Math 6010 • Linear Models
Spring 2008 • Question 1
Question
Spring 2008 • Question 1
Let \(X\) and \(Y\) have joint density \[ f(x,y)=g\left (\sqrt {x^2+y^2}\right ),\qquad (x,y)\in \mathbb {R}^2, \] for some function \(g\). Show that \(Z=X/Y\) has a Cauchy density.