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Introduction to Probability With R

Textbook

By: Kenneth Baclawski

363 pages, Figs, illus, tabs

Chapman & Hall (CRC Press)

Hardback | Feb 2008 | #171413 | ISBN-13: 9781420065213
Availability: Usually dispatched within 6 days Details
NHBS Price: £64.99 $83/€78 approx

About this book

Based on the popular probability course by Gian-Carlo Rota of MIT, Probability and Random Processes with R provides a calculus-based introduction to probability. The text systemically motivates and organizes the standard distributions that most often occur in probability using physical processes. Presenting a probabilistic approach that builds on other approaches such as geometry and physical processes, the book addresses sets, events, and probability; finite processes; random variables; statistics and normal distribution; conditional probability; the Poisson process; entropy and information; Markov chains; Markov processes; Bayesian networks; and the Bayesian web. Various exercises and examples compare different perspectives.

! beginners should find the informal and nonthreatening presentation of the basic ideas very useful ! A more advanced student could use the book as an extra source of intriguing mathematical examples, as could an instructor searching for interesting items to throw into a more conventional course. ! a very interesting book ! --Technometrics, May 2009, Vol. 51, No. 2 Generally, I was very impressed with this text. It gives a sold introduction to probability with many interesting applications. One of its strengths is its material on stochastic processes. --Jim Albert, Bowling Green State University, The American Statistician, May 2009, Vol. 63, No. 2 ! a welcome addition. !The book is clearly written and very well-organized and it stems in part from a popular course at MIT taught by the late Gian-Carlo Rota, which was originally designed in conjunction with the author of this book. The book goes well beyond the MIT course in making extensive use of computation and R. ! It would serve as an exemplary test for the first semester of a two-semester course on probability and statistics. Introduction to Probability with R is a well-organized course in probability theory. ! --Journal of Statistical Software, April 2009 This advanced undergraduate textbook is a pleasure to read and this reviewer will definitely consider it next time he teaches the subject. The programming language R is an open-source, freely downloadable software package that is used in the book to illustrate various examples. However, the book is well usable even if you do not have the time to include too much programming in your class. All programs of the book, and several others, are downloadable from the book's website. ! the exercises of this book are a lot of fun! They often have some historical background, they tell a story, and they are never routine. Every chapter also starts with historical background, helping the student realize that this subject was developed by actual people. All classic topics that you would want to cover in an introductory probability class are covered. ! Another aspect in which the book stands out among the competition is that discrete probability gets its due treatment. ! --Miklos Bona, University of Florida, MAA Reviews, June 2008 !a broad spectrum of probability and statistics topics ranging from set theory to statistics and the normal distribution to Poisson process to Markov chains. The author has covered each topic with an ample depth and with an appreciation of the problems faced by the modern world. The book contains a rich collection of exercises and problems ! an excellent introduction to the open source software R is given in the book. ! This book showcases interesting, classic puzzles throughout the text, and readers can also get a glimpse of the lives and achievements of important pioneers in mathematics. ! --From the Foreword, Tianhua Niu, Brigham and Women's Hospital, Harvard Medical School, and Harvard School of Public Health, Boston, Massachusetts, USA


Contents

FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variables Order Statistics The Concept of a General Random Variable Joint Distribution and Joint Density Mean, Median and Mode The Uniform Process Table of Probability Distributions Scale Invariance Statistics and the Normal Distribution Variance Bell-Shaped Curve The Central Limit Theorem Significance Levels Confidence Intervals The Law of Large Numbers The Cauchy Distribution Conditional Probability Discrete Conditional Probability Gaps and Runs in the Bernoulli Process Sequential Sampling Continuous Conditional Probability Conditional Densities Gaps in the Uniform Process The Algebra of Probability Distributions The Poisson Process Continuous Waiting Times Comparing Bernoulli with Uniform The Poisson Sample Space Consistency of the Poisson Process Randomization and Compound Processes Randomized Bernoulli Process Randomized Uniform Process Randomized Poisson Process Laplace Transforms and Renewal Processes Proof of the Central Limit Theorem Randomized Sampling Processes Prior and Posterior Distributions Reliability Theory Bayesian Networks Entropy and Information Discrete Entropy The Shannon Coding Theorem Continuous Entropy Proofs of Shannon's Theorems Markov Chains The Markov Property The Ruin Problem The Network of a Markov Chain The Evolution of a Markov Chain The Markov Sample Space Invariant Distributions Monte Carlo Markov Chains appendix A: Random Walks Fluctuations of Random Walks The Arcsine Law of Random Walks Appendix B: Memorylessness and Scale-Invariance Memorylessness Self-Similarity References Index Exercises and Answers appear at the end of each chapter.

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