This is an archived course. A more recent version may be available at ocw.mit.edu.

Readings

This section provides the required and recommended readings for the course. Reading assignments for specific topics are also presented.

Main Textbook (Required)

Amazon logo 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:

Amazon logo Williams, D. Probability with Martingales. Cambridge, UK: Cambridge University Press, 1991. ISBN: 0521406056.

The course syllabus is a proper superset of the MIT course 6.041/6.431 syllabus. For a more accessible coverage of that material:

Amazon logo 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:

Amazon logo 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:

Amazon logo Breiman, Leo. Probability (Classics in Applied Mathematics, No. 7). Reprint ed. Philadelphia, PA: Soc. for Industrial & Applied Math, 1992. ISBN: 0898712963.

Amazon logo Karr, Alan F. Probability (Springer Texts in Statistics). New York, NY: Springer-Verlag, 1993. ISBN: 0387940715.

And an excellent but more mathematically advanced reference:

Amazon logo Durrett, Richard. Probability: Theory and Examples. 3rd ed. Belmont, CA: Duxbury Press, 2004. ISBN: 0534424414.

Readings for Specific Topics

The abbreviations presented in the table below refer to the following books:

Amazon logo GS = Grimmett, G. R., and D. R. Stirzaker. Probability and Random Processes. 3rd ed. New York, NY: Oxford University Press, 2001. ISBN: 0198572220.

Amazon logo BT = Bertsekas, D. P., and J. N. Tsitsiklis. Introduction to Probability. Belmont, MA: Athena Scientific Press, 2002. ISBN: 188652940X.

SESĀ # 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)