Basic Notions of Probability Theory

This initial chapter covers background material that every serious student of applied probability should master. In no sense is the chapter meant as a substitute for a previous course in applied probability or for a future course in measure-theoretic probability. Our comments are merely meant as reminders and as a bridge. Many mathematical facts will be stated without proof. This is unsatisfactory, but it is even more unsatisfactory to deny students the most powerful tools in the probabilist’s toolkit. Quite apart from specific tools, the language and intellectual perspective of modern probability theory also furnish an intuitive setting for solving practical problems. Probability involves modes of thought that are unique within mathematics.