This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and renewal theory. Many new introductory problems and exercises have also been added. This book combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The book begins with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation. Also included is a chapter on statistical inference with a focus on Bayesian statistics, which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time are also discussed within the book. More than 400 examples are interspersed throughout to help illustrate concepts and theory and to assist readers in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter.

"What are the chances?"

Find out in this entertaining exploration ofprobabilities in our everyday lives

"If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations."-- Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Math Instinct

"A delightful guide to the sometimes counterintuitive discipline of probability. Olofsson points out major ideas here, explains classic puzzles there, and everywhere makes free use of witty vignettes to instruct and amuse."-- John Allen Paulos, Temple University, author of Innumeracy and A Mathematician Reads the Newspaper

"Beautifully written, with fascinating examples and tidbits of information. Olofsson gently and persuasively shows us how to think clearly about the uncertainty that governs our lives."-- John Haigh, University of Sussex, author of Taking Chances: Winning with Probability

From probable improbabilities to regular irregularities, "Probabilities: The Little Numbers That Rule Our Lives "investigates the often-surprising effects of risk and chance in our everyday lives. With examples ranging from WWII espionage to the O. J. Simpson trial, from bridge to blackjack, from Julius Caesar to Jerry Seinfeld, the reader is taught how to think straight in a world of randomness and uncertainty. Throughout the book, readers learn: Why it is not that surprising for someone to win the lottery twiceHow a faulty probability calculation forced an innocent woman to spend three years in prisonHow to place bets if you absolutely insist on gamblingHow a newspaper turned an opinion poll into one of the greatest election blunders in history

Educational, eloquent, and entertaining, "Probabilities: The Little Numbers That Rule Our Lives" is the ideal companion for anyone who wants to obtain a better understanding of the mathematics of chance.

Praise for the First Edition "If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations." - Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Unfinished Game From probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featuring a timely update, the Second Edition continues to be the go-to guidebook for an entertaining presentation on the mathematics of chance and uncertainty. The new edition develops the fundamental mathematics of probability in a unique, clear, and informal way so readers with various levels of experience with probability can understand the little numbers found in everyday life. Illustrating the concepts of probability through relevant and engaging real-world applications, the Second Edition features numerous examples on weather forecasts, DNA evidence, games and gambling, and medical testing. The revised edition also includes: The application of probability in finance, such as option pricing The introduction of branching processes and the extinction of family names An extended discussion on opinion polls and Nate Silver's election predictions Probabilities: The Little Numbers That Rule Our Lives, Second Edition is an ideal reference for anyone who would like to obtain a better understanding of the mathematics of chance, as well as a useful supplementary textbook for students in any course dealing with probability.