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It is now over 10 years since the publication of the first edition of “Probability with R.” Back then we had just begun to hear of smartphones, fitbits, apps, and Bluetooth; machine learning was in its infancy. It is timely to address how probability applies to new developments in computing. The applications and examples of the first edition are beginning to look somewhat passé and old fashioned. Here, therefore, we offer an updated and extended version of that first edition.

This second edition is still intended to be a first course in probability, addressed to students of computing and related disciplines. As in the first edition, we favor experimentation and simulation rather than the traditional mathematical approach. We continue to rely on the freely downloadable language R, which has of course evolved over the past 10 years.

Our R programs are integrated throughout the text, to illustrate the concepts of probability, to simulate distributions, and to explore new problems. We have been mindful to avoid as far as is possible mathematical details, instead encouraging students to investigate for themselves, through experimentation and simulation in R. Algebraic derivations, when deemed necessary, are developed in the appendices.

In this second edition, all chapters have been revised and updated. Examples and applications of probability in new areas of computing, as well as exercises and projects, have been added to most chapters. The R code has been improved and expanded, by using procedures and functions that have become available in recent years. Extended use of loops and curve facilities to generate graphs with differing parameters have tidied up our approach to limiting distributions.

Briefly the changes in this second edition are

1 Part I, “The R Language” now contains:new and improved R procedures, and an introduction to packages and interfaces (Chapter 1);examples on apps to illustrate outliers, to calculate statistics in a data frame and statistics appropriate to skewed data (Chapter 2);an introduction to linear regression, with a discussion of its importance as a tool in machine learning. We show how to obtain the line of best fit with the training set, and how to use the testing set to examine the suitability of the model. We also include extra graphing facilities (Chapter 3).

2 In Part II, “Fundamentals of Probability”:Chapter 4 has been extended with extra examples on password recognition and new R functions to address hash table collision, server overload and the general allocation problem;The concept of “independence” has now been extended from pairs to multiply variables (Chapter 6);Chapter 7 contains new material on machine learning, notably the use of Bayes' theorem to develop spam filters.

3 Part III “Discrete Distributions” now includes:an introduction to bivariate discrete distributions, and programming techniques to handle large conditional matrices (Chapter 9);an algorithm to simulate the Markov property of the geometric distribution (Chapter 10);an extension of the reliability model of Chapter 8 to the general reliability model (Chapter 11);an update of the lottery rules (Chapter 12);an extended range of Poisson applications such as network failures, website hits, and virus attacks (Chapter 13).

4 In Part IV “Continuous Distributions”:Chapters 16 and 17 have been reorganized. Chapter 17 now concentrates entirely on queues while Chapter 16 is extended to deal with the applications of the exponential distribution to lifetime models.

5 Part V “Tailing Off”has extra exercises on recent applications of computing.

6 We have added three new appendices: Appendix A gives the data set used in Part I, Appendix B derives the coefficients of the line of best fit and Appendix F contains new proofs of the Markov and Chebyshev inequalities. The original appendices A, B, and C have been relabeled C, D, and E.

7 A separate index containing R commands and functions has been added.

All errors in the first edition have hopefully been corrected. I apologize in advance for any new errors that may escape my notice in this edition; should they arise, they will be corrected in the companion website.

Jane M. Horgan

Dublin City University

Ireland

2019