| SES # | TOPICS | READINGS |
|---|---|---|
| R1 | Background Material from Analysis | Handout (PDF) |
| L2 | Probability Measure, Lebesgue Measure | Handout (PDF) GS, 1.1-1.3 |
| L3 | Conditioning, Bayes Rule, Independence, Borel-Cantelli-Lemmas | GS, 1.4-1.7 |
| L4 | Counting | BT, 1.6 |
| L5 | Measurable Functions, Random Variables, Cumulative Distribution Functions | Handout (PDF) GS, 2 and 3.1-3.8 |
| L8 | Continuous Random Variables, Expectation | GS, 4.1-4.6 |
| L10 | Derived Distributions | GS, 4.7-4.8 |
| L11 | Abstract Integration | GS, 5.6 |
| L14 | Transforms: Moment Generating and Characteristic Functions | GS, 5.1, 5.7-5.9 |
| L15 | Multivariate Normal | Handout (PDF) GS, 4.9 |
| L17 | Weak Law of Large Numbers Central Limit Theorem | Handout from BT, chapter 7 GS, 5.10 (up to p. 196) |
| L19 | Poisson Process | Handout from BT, chapter 5 GS, 6.8 (up to p. 249) |
| L20 | Finite-state Markov Chains | Handout from BT, chapter 6 Handout on Markov Chains (PDF) GS, 6.1 |
| L23 | Convergence of Random Variables | GS, 7.1-7.4 The latter half of section 7.3 (Zero-one Law, etc.) will not be on the final exam. |
| L24 | Strong Law of Large Numbers | GS, 7.1-7.4 The latter half of section 7.3 (Zero-one Law, etc.) will not be on the final exam. |
| L25 | L2 Theory of Random Variables Construction of Conditional Expectations | GS, 7.9 (not on the final exam) |
Table of Contents
Study Materials
Readings
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This section provides the required and recommended readings for the course. Reading assignments for specific topics are also presented.
Main Textbook (Required)
Grimmett, G. R., and D. R. Stirzaker. Probability and Random Processes. 3rd ed. New York, NY: Oxford University Press, 2001. ISBN: 0198572220.
Recommended
For a concise, crisp, and rigorous treatment of the theoretical topics to be covered:
Williams, D. Probability with Martingales. Cambridge, UK: Cambridge University Press, 1991. ISBN: 0521406056.
The course syllabus is a proper superset of the 6.041/6.431 syllabus. For a more accessible coverage of that material:
Bertsekas, D. P., and J. N. Tsitsiklis. Introduction to Probability. Belmont, MA: Athena Scientific Press, 2002. ISBN: 188652940X.
Other References
A classic reference; fairly advanced at times, but without measure theory:
Feller, William. An Introduction to Probability Theory and Its Applications. Vol. 1. 3rd ed. New York, NY: Wiley, 1968. ISBN: 0471257087.
Well-written expositions of the more mathematical topics in this course, though generally more abstract and detailed:
Breiman, Leo. Probability (Classics in Applied Mathematics, No. 7). Reprint ed. Philadelphia, PA: Soc. for Industrial & Applied Math, 1992. ISBN: 0898712963.
Karr, Alan F. Probability (Springer Texts in Statistics). New York, NY: Springer-Verlag, 1993. ISBN: 0387940715.
And an excellent but more mathematically advanced reference:
Durrett, Richard. Probability: Theory and Examples. 3rd ed. Belmont, CA: Duxbury Press, 2004. ISBN: 0534424414.
The abbreviations presented in the table below refer to the following books:
GS = Grimmett, G. R., and D. R. Stirzaker. Probability and Random Processes. 3rd ed. New York, NY: Oxford University Press, 2001. ISBN: 0198572220.
BT = Bertsekas, D. P., and J. N. Tsitsiklis. Introduction to Probability. Belmont, MA: Athena Scientific Press, 2002. ISBN: 188652940X.