A note while walking through the book “A Rigorous Look at Probability Theory”, and other classic statistics books, e.g. “Probability and Statistics” by Morris DeGroot et al.

• Contents.

Preface

xxx

Draft Notes

The Definition of Probability

xxx

Intuitive definition

xxx

Measure-theoretic definition

xxx

Inequalities

In the book of “Introduction to Probability” at Harvard University, I study a little bit about probability inequalities, which might be used in learning CS229 notes of the Stanford Machine Learning course.

Theorem 10.1.1 (Cauchy-Schwarz). For any r.v.s $X$ and $Y$with finite variances:

$$ \vert E(XY) \vert \leq \sqrt{E(X^2)E(Y^2)} $$

• Proof.
• Comment.

Advanced Topics

Robust Statistics