6.041 | Spring 2006 | Undergraduate

Probabilistic Systems Analysis and Applied Probability


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.

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  

Course Info

As Taught In
Spring 2006
Learning Resource Types
Simulation Videos
Problem Sets with Solutions
Exams with Solutions
Lecture Notes