The Ratios of Functions of Random Variables

Given the joint probability density function (pdf), pX(xl, ..., xN), of the random variables x1, xN, a new method is developed for determining the pdf of the ratio f(X)lg(X) where f and g are arbitrary functions. The method is then applied to calculate the pdf of x1 lx2 where x1 and x2 are correlated Gaussians with arbitrary means and variances.