Summary: Chapter 2
A Quick Review of Probability
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 , and Timo
Sepp¨al¨ainen's notes on probability theory that serve a similar purpose . Any
student who finds this material difficult should review an introductory probability
book such as Sheldon Ross's A first course in probability , 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