Sum of products functional equation

In this lesson we deal with a special functional equation that allow us to build some interesting models. The name comes from the fact that the equation is the sum of products of functions of x and functions of y. In particular, we present the problem of designing a cover of a sports building suvh that the sections parallel to the coordinate axes are second degree polynomials, and the most general bivariate distribution with normal conditionals, that is an important problem. It can be generalized to other conditional families.