The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
Life can be unpredictable. And the more you can predict, the more control you will have over your own life. From calculating the health risks of smoking a pack of cigarettes a day to deciding on the best investments for your money, probabilities play a part in nearly all aspects of everyday life. Now, physics professor John D. McGervey puts all the facts and figures at your fingertips to help you make savvy, informed choices at home, at work, and at play. You will learn how the author believes you can: * Increase your chances of winning blackjack, contract bridge, horse racing, sports betting, and more * Get the most for your dollar when investing or buying insurance * Judge the risks of such common activities as smoking, using drugs, owning a handgun, and driving without a seat belt * Avoid faulty gambling systems and identify misleading statistics that can be used to draw you into poor investments * And much more. Inside you'll find a lively, entertaining, enlightening approach to minimizing your risks and maximizing your results -- simple strategies designed to give you the edge in life.
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.
Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
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 twice How a faulty probability calculation forced an innocent woman to spend three years in prison How to place bets if you absolutely insist on gambling How 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.
A self-study guide for practicing engineers, scientists, and students, this book offers practical, worked-out examples on continuous and discrete probability for problem-solving courses. It is filled with handy diagrams, examples, and solutions that greatly aid in the comprehension of a variety of probability problems.
Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. Exercises with some solutions. Summary. 1973 edition.
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
