A Quick Review of Probability These notes are not intended to be a comprehensive introduction to the theory of Summary: Chapter 2 A Quick Review of Probability Theory These notes are not intended to be a comprehensive introduction to the theory of probability. Instead, they constitute a brief introduction that should be sufficient to allow a student to understand the stochastic models they will encounter in later chapters. These notes were heavily influenced by Sheldon Ross's text [11], and Timo Sepp¨al¨ainen's notes on probability theory that serve a similar purpose [12]. Any student who finds this material difficult should review an introductory probability book such as Sheldon Ross's A first course in probability [11], which is on reserve in the Math library. 2.1 The Probability Space Probability theory is used to model experiments (defined loosely) whose outcome can not be predicted with certainty beforehand. For any such experiment, there is a triple (, F, P), called a probability space, where ˇ is the sample space, ˇ F is a collection of events, ˇ P is a probability measure. We will consider each in turn. 2.1.1 The sample space Collections: Mathematics