Introduction to Probability
by Anderson, Seppäläinen,
Valkó

Table of Contents
1. Experiments with random outcomes
2. Conditional probability and independence
3. Random variables
4. Approximations of the binomial distribution
5. Transforms and transformations
6. Joint distribution of random variables
7. Sums and symmetry
8. Expectation and variance in the multivariate setting
9. Tail bounds and limit theorems
10. Conditional distribution
Appendix A. Things to know from calculus
Appendix B. Set notation and operations
Appendix C. Counting
Appendix D. Sums, products and series
Appendix E. Table of values for Φ(x)
Appendix F. Table of common probability distributions

The authors welcome comments and corrections to the text.
Corrections
and clarifications (last updated: 3/14/18)
Part of the Cambridge
Mathematical Textbooks series.
Cambridge University Press page
Amazon page