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.
ISBN-13: 9781108415859
Media Type: Hardcover
Publisher: Cambridge University Press
Publication Date: 11-02-2017
Pages: 442
Product Dimensions: 7.28(w) x 10.28(h) x 0.91(d)
Series: Cambridge Mathematical Textbooks
David F. Anderson is a Professor of Mathematics at the University of Wisconsin, Madison. His research focuses on probability theory and stochastic processes, with applications in the biosciences. He is the author of over thirty research articles and a graduate textbook on the stochastic models utilized in cellular biology. He was awarded the inaugural Institute for Mathematics and its Applications (IMA) Prize in Mathematics in 2014, and was named a Vilas Associate by the University of Wisconsin, Madison in 2016.
Timo Seppäläinen is the John and Abigail Van Vleck Chair of Mathematics at the University of Wisconsin-Madison. He is the author of over seventy research papers in probability theory and a graduate textbook on large deviation theory. He is an elected Fellow of the Institute of Mathematical Statistics. He was an IMS Medallion Lecturer in 2014, an invited speaker at the 2014 International Congress of Mathematicians, and a 2015–16 Simons Fellow.
Benedek Valkó is a Professor of Mathematics at the University of Wisconsin, Madison. His research focuses on probability theory, in particular in the study of random matrices and interacting stochastic systems. He has published over thirty research papers. He has won a National Science Foundation (NSF) CAREER award and he was a 2017–18 Simons Fellow.
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.
