Generating Functions and Characteristic Functions
These functions are of considerable use in theoretical probability, i.e., proving probability theorems. They are also of use to us when we wish to put two distributions together. Consider x = x 1 + x 2 + ... + x n, where x 1 is distributed according to one distribution, x 2 according to another, etc. Sometimes the number of distributions is not fixed, but distributed according to some random distribution also. In the present chapter, we will consider several examples of applications of this kind.