Suppose we are interested in not only the mean and variance of the transformation but the whole distribution of the transformed random variables. We considered this problem in one dimension in Chapter 4 and gave various methods for obtaining the cdf and pdf. The distribution function method extends immediately to higher dimensions, but in practice is hard to use, so we focus on the density method. To keep the presentation simple for the general detail we focus on bivariate transformations. (The extension to higher dimensions is straight-forward conceptually but messy mathematically.)