Brief notes on Probability and Martingales

These are brief lecture notes for a course on Probability and Martingales developed when I (Gautam Iyer) taught it at Carnegie Mellon University. These notes intentionally only list definitions, and statements of results, and problems, and occasionally brief sketches of proofs. I do motivation, intuition, and complete proofs in class. There are also several comprehensive references for this material so I don’t plan to include them in these notes.

Contents

• Probability spaces and Random Variables
• Conditional Probability and Independence
• Expectations of Random Variables
• Law of Large Numbers
• Continuous Random Variables
• Central limit theorem

Source Code

The source code is available on Codeberg.

The notes are written in Markdown, and converted to HTML5 using the Python script md-to-html. It should be viewable on most modern browsers, but I only test it on Firefox.

Licence

Brief notes on Probability and Martingales © 2026 by Gautam Iyer is licensed under Creative Commons Attribution-NonCommercial 4.0 International .

You may adapt and share this work for non-commercial purposes, provided you cite it appropriately. The full terms are in the licence deed.