Courses:

Probabilistic Systems Analysis and Applied Probability >> Content Detail



Study Materials



Readings

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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 #TOPICSReadings
L1Probability Models and AxiomsSections 1.1-1.2
L2Conditioning and Bayes' RuleSections 1.3-1.4
L3IndependenceSection 1.5
L4CountingSection 1.6
L5Discrete Random Variables; Probability Mass Functions; ExpectationsSections 2.1-2.4
L6Conditional Expectation; ExamplesSections 2.4-2.6
L7Multiple Discrete Random VariablesSection 2.7
L8Continuous Random Variables - ISections 3.1-3.3
L9Continuous Random Variables - IISections 3.4-3.5
L10Continuous Random Variables and Derived DistributionsSection 3.6
Quiz 1 (Covers up to Lec #1-8 Inclusive)
L11More on Continuous Random Variables, Derived Distributions, ConvolutionSection 4.2
L12TransformsSection 4.1
L13Iterated ExpectationsSections 4.3
L13ASum of a Random Number of Random VariablesSection 4.4
L14Prediction; Covariance and CorrelationSections 4.5-4.6
L15Weak Law of Large NumbersSections 7.1-7.3
Quiz 2 (Covers up to and Including Lec #14)
L16Bernoulli ProcessSection 5.1
L17Poisson ProcessSection 5.2
L18Poisson Process ExamplesSection 5.2
L19Markov Chains - ISections 6.1-6.2
L20Markov Chains - IISection 6.3
L21Markov Chains - IIISection 6.4
L22Central Limit TheoremSection 7.4
L23Central Limit Theorem (cont.), Strong Law of Large NumbersSection 7.5
Final Exam

 








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