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Fundamentals of Probability >> Content Detail



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.



Readings for Specific Topics


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.


SES #TOPICSREADINGS
R1Background Material from AnalysisHandout (PDF)
L2Probability Measure, Lebesgue MeasureHandout (PDF)

GS, 1.1-1.3
L3Conditioning, Bayes Rule, Independence, Borel-Cantelli-LemmasGS, 1.4-1.7
L4CountingBT, 1.6
L5Measurable Functions, Random Variables, Cumulative Distribution FunctionsHandout (PDF)

GS, 2 and 3.1-3.8
L8Continuous Random Variables, ExpectationGS, 4.1-4.6
L10Derived DistributionsGS, 4.7-4.8
L11Abstract IntegrationGS, 5.6
L14Transforms: Moment Generating and Characteristic FunctionsGS, 5.1, 5.7-5.9
L15Multivariate NormalHandout (PDF)

GS, 4.9
L17Weak Law of Large Numbers

Central Limit Theorem
Handout from BT, chapter 7

GS, 5.10 (up to p. 196)
L19Poisson ProcessHandout from BT, chapter 5

GS, 6.8 (up to p. 249)
L20Finite-state Markov ChainsHandout from BT, chapter 6

Handout on Markov Chains (PDF)

GS, 6.1
L23Convergence of Random VariablesGS, 7.1-7.4

The latter half of section 7.3 (Zero-one Law, etc.) will not be on the final exam.
L24Strong Law of Large NumbersGS, 7.1-7.4

The latter half of section 7.3 (Zero-one Law, etc.) will not be on the final exam.
L25L2 Theory of Random Variables

Construction of Conditional Expectations
GS, 7.9 (not on the final exam)

 








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