6.041 | Spring 2006 | Undergraduate

Probabilistic Systems Analysis and Applied Probability

Lecture Notes

L1 Probability Models and Axioms (PDF)
L2 Conditioning and Bayes’ Rule (PDF)
L3 Independence (PDF)
L4 Counting Sections (PDF)
L5 Discrete Random Variables; Probability Mass Functions; Expectations (PDF)
L6 Conditional Expectation; Examples (PDF)
L7 Multiple Discrete Random Variables (PDF)
L8 Continuous Random Variables - I (PDF)
L9 Continuous Random Variables - II (PDF)
L10 Continuous Random Variables and Derived Distributions (PDF)
L11 More on Continuous Random Variables, Derived Distributions, Convolution (PDF)
L12 Transforms (PDF)
L13 Iterated Expectations (PDF)
L13A Sum of a Random Number of Random Variables (PDF)
L14 Prediction; Covariance and Correlation (PDF)
L15 Weak Law of Large Numbers (PDF)
L16 Bernoulli Process (PDF)
L17 Poisson Process (PDF)
L18 Poisson Process Examples (PDF)
L19 Markov Chains - I (PDF)
L20 Markov Chains - II (PDF)
L21 Markov Chains - III (PDF)
L22 Central Limit Theorem (PDF)
L23 Central Limit Theorem (cont.), Strong Law of Large Numbers (PDF)

Course Info

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