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This section contains the lecture notes for the course. Each set of notes refer to reading assignments for the course textbook, Introduction to Probability. written by Professors John Tsitsiklis and Dimitri Bertsekas. Some of the slides in the notes are intentionally left blank, used by the instructors to work through material with students during class.
Lecture notes files.
| Ses # |
Topics |
| L1 |
Probability Models and Axioms (PDF) |
| L2 |
Conditioning and Bayes' Rule (PDF) |
| L3 |
Independence (PDF) |
| L4 |
Counting (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, Sum of a Random Number of Random Variables (PDF) |
| L14 |
Prediction; Covariance and Correlation (PDF) |
| L15 |
Bernoulli Process (PDF) |
| L16 |
Poisson Process (PDF) |
| L17 |
Poisson Process Examples (PDF) |
| L18 |
Markov Chains - I (PDF) |
| L19 |
Markov Chains - II (PDF) |
| L20 |
Markov Chains - III (PDF) |
| L21 |
Weak Law of Large Numbers (PDF) |
| L22 |
Central Limit Theorem (PDF) |
| L23 |
Strong Law of Large Numbers (PDF) |
| L24 |
Interactive Exploration |