Probability & Statistics

These are my notes from Mark Maxwell’s courses — Probability I and Introduction to Mathematical Statistics — and his textbook, Probability & Statistics with Applications, Second Edition. I’ve stitched them together into one reference (with much help from Claude).

There’s a clean way to think about the difference between probability and statistics. Probability reasons forward: given a known model of the world, what’s the chance of seeing some outcome? Statistics reasons backward: given outcomes we actually observed, what was the model that produced them?