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 # 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