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Introduction to Probability with R

Kenneth Baclawski
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Texts in Statistical Science 75
[Reviewed by
Miklós Bóna
, on

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.

While there are not as many exercises than in some competing textbooks, 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. Statistics get one chapter, related to the normal distribution. Another aspect in which the book stands out among the competition is that discrete probability gets its due treatment.

When can I teach this class next?

Miklós Bóna is Associate Professor of Mathematics at the University of Florida.

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
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
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
Exercises and Answers appear at the end of each chapter.