Introduction to Probability

An introductory probability textbook with the right balance between mathematical precision, probabilistic intuition, and concrete applications.

David F. Anderson (Author), Timo Seppäläinen (Author), Benedek Valkó (Author)

9781108415859, Cambridge University Press

Hardback, published 2 November 2017

442 pages, 45 b/w illus. 48 colour illus. 600 exercises
26.1 x 18.5 x 2.3 cm, 1.08 kg

'The content is beautifully set out, with clear diagrams … Definitions, theorems and key facts are highlighted. The precise natures of general ideas are carefully explained and motivated by diverse examples. Following each chapter, the reader is led gently into set exercises, with explicit signposts initially and more challenging problems at the end.' John Haigh, Significance

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

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 ?(x)
Appendix F. Table of common probability distributions.

Subject Areas: Stochastics [PBWL], Probability & statistics [PBT]