1. Probability Spaces

Summary

In this chapter, we study the paradigm of the random experiment and its mathematical model, the probability space. The main objects in this model are sample spaces, events, random variables, and probability measures. We also study several concepts of fundamental importance: conditional probability and independence, and we study several modes of convergence that are appropriate for random variables.

Topics

1. Random Experiments
2. Events and Random Variables
3. Probability Measures
4. Conditional Probability
5. Independence
6. Convergence
7. Measure Theory

• Answers to selected exercises

Applets

• Coin Sample Experiment
• Buffon's Coin Experiment
• Dice Sample Experiment
• Dice Experiment
• Card Sample Experiment
• Die-Coin Experiment
• Coin-Die Experiment
• Venn Diagram Applet

Topics in PDF Format

• Random Experiments
• Events and Random Variables
• Probability Measures
• Conditional Probability
• Independence
• Convergence
• Measure Theory
• Answers to selected exercises

External Resources

• An Introduction to Probability Theory and It's Applications, Volume 1 by William Feller. One of the best references on probability.
• A First Course in Probability by Sheldon Ross. An excellent book on elementary probability with a wealth of examples and exercises.
• The Essentials of Probability by Richard Durrett. A compact treatment of elementary probability.
• Probability and Measure, by Patrick Billingsley. A higher level measure-theoretic treatment of probability.
• Games, Gods and Gambling, by Florence David. An excellent treatment of the early history of probability.
• History of Mathematics. The definitive site for the historical information about probability.

Quote

• The most important questions of life are, for the most part, really only problems of probability.--Pierre Simon Laplace