Required Text
This section contains the reading assignments from the course textbook:
Bertsekas, Dimitri P., and John N. Tsitsiklis. Introduction to Probability. Belmont, MA: Athena Scientific Press, June 2002. ISBN: 188652940X.
Recommended Texts
The following books cover many of the topics in this course, although in a different style. You may wish to consult them to get a different prospective on particular topics.
Drake, A. Fundamentals of Applied Probability Theory. New York, NY: McGraw-Hill, 1988. ISBN: 0070178151.
Ross, S. A First Course in Probability. Upper Saddle River, NJ: Prentice Hall, 2005. ISBN: 0131856626.
Readings by Session
| Ses # | TOPICS | Readings |
|---|---|---|
| L1 | Probability Models and Axioms | Sections 1.1-1.2 |
| L2 | Conditioning and Bayes' Rule | Sections 1.3-1.4 |
| L3 | Independence | Section 1.5 |
| L4 | Counting | Section 1.6 |
| L5 | Discrete Random Variables; Probability Mass Functions; Expectations | Sections 2.1-2.4 |
| L6 | Conditional Expectation; Examples | Sections 2.4-2.6 |
| L7 | Multiple Discrete Random Variables | Section 2.7 |
| L8 | Continuous Random Variables - I | Sections 3.1-3.3 |
| L9 | Continuous Random Variables - II | Sections 3.4-3.5 |
| L10 | Continuous Random Variables and Derived Distributions | Section 3.6 |
| Quiz 1 (Covers up to Lec #1-8 Inclusive) | ||
| L11 | More on Continuous Random Variables, Derived Distributions, Convolution | Section 4.2 |
| L12 | Transforms | Section 4.1 |
| L13 | Iterated Expectations | Sections 4.3 |
| L13A | Sum of a Random Number of Random Variables | Section 4.4 |
| L14 | Prediction; Covariance and Correlation | Sections 4.5-4.6 |
| L15 | Weak Law of Large Numbers | Sections 7.1-7.3 |
| Quiz 2 (Covers up to and Including Lec #14) | ||
| L16 | Bernoulli Process | Section 5.1 |
| L17 | Poisson Process | Section 5.2 |
| L18 | Poisson Process Examples | Section 5.2 |
| L19 | Markov Chains - I | Sections 6.1-6.2 |
| L20 | Markov Chains - II | Section 6.3 |
| L21 | Markov Chains - III | Section 6.4 |
| L22 | Central Limit Theorem | Section 7.4 |
| L23 | Central Limit Theorem (cont.), Strong Law of Large Numbers | Section 7.5 |
| Final Exam |