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Preface

Digitization of DeGroot and Schervish, Probability and Statistics (Fourth Edition), by Jeff Jacobs, Assistant Teaching Professor of Data Science and Analytics, Georgetown University.

Changes in the Digitized Version

To match the notation we’re using in DSAN 5100, I have made the following changes (which could be undone via a find-and-replace, if you want to change the format back to the original textbook format):

Changes to the Fourth Edition

Some other changes that readers will notice:

How to Use This Book

The text is somewhat long for complete coverage in a one-year course at the undergraduate level and is designed so that instructors can make choices about which topics are most important to cover and which can be left for more in-depth study. As an example, many instructors wish to deemphasize the classical counting arguments that are detailed in Sections 1.7 Counting Methods1.9 Multinomial Coefficients. An instructor who only wants enough information to be able to cover the binomial and/or multinomial distributions can safely discuss only the definitions and theorems on permutations, combinations, and possibly multinomial coefficients. Just make sure that the students realize what these values count, otherwise the associated distributions will make no sense. The various examples in these sections are helpful, but not necessary, for understanding the important distributions. Another example is 3.9 Functions of Two or More Random Variables on functions of two or more random variables. The use of Jacobians for general multivariate transformations might be more mathematics than the instructors of some undergraduate courses are willing to cover. The entire section could be skipped without causing problems later in the course, but some of the more straightforward cases early in the section (such as convolution) might be worth introducing. The material in Sections sec-9-2sec-9-4 on optimal tests in one-parameter families is pretty mathematics, but it is of interest primarily to graduate students who require a very deep understanding of hypothesis testing theory. The rest of sec-9 covers everything that an undergraduate course really needs.

In addition to the text, the publisher has an Instructor’s Solutions Manual, available for download from the Instructor Resource Center at www.pearsonhighered.com/irc, which includes some specific advice about many of the sections of the text.

I have taught a year-long probability and statistics sequence from earlier editions of this text for a group of mathematically well-trained juniors and seniors. In the first semester, I covered what was in the earlier edition but is now in the first five chapters (including the material on Markov chains) and parts of sec-6. In the second semester, I covered the rest of the new sec-6, Chapters sec-7sec-9, Sections sec-11-1-sec-11-5, and sec-12. I have also taught a one-semester probability and random processes course for engineers and computer scientists. I covered what was in the old edition and is now in Chapters Chapter 1: Introduction to Probabilitysec-6 and sec-12, including Markov chains, but not Jacobians. This latter course did not emphasize mathematical derivation to the same extent as the course for mathematics students.

A number of sections are designated with an asterisk (*). This indicates that later sections do not rely materially on the material in that section. This designation is not intended to suggest that instructors skip these sections. Skipping one of these sections will not cause the students to miss definitions or results that they will need later. The sections are 2.4 The Gambler’s Ruin Problem, 3.10 Markov Chains, 4.8 Utility, sec-7-7, sec-7-8, sec-7-9, sec-8-6, sec-8-8, sec-9-2, sec-9-3, sec-9-4, sec-9-8, sec-9-9, sec-10-6, sec-10-7, sec-10-8, sec-11-4, sec-11-7, sec-11-8, and sec-12-5. Aside from cross-references between sections within this list, occasional material from elsewhere in the text does refer back to some of the sections in this list. Each of the dependencies is quite minor, however.

Most of the dependencies involve references from sec-12 back to one of the optional sections. The reason for this is that the optional sections address some of the more difficult material, and simulation is most useful for solving those difficult problems that cannot be solved analytically. Except for passing references that help put material into context, the dependencies are as follows:

Supplements

The text is accompanied by the following supplementary material:

The person who checked the accuracy of the book was Anda Gadidov, Kennesaw State University. I would also like to thank my colleagues at Carnegie Mellon University, especially Anthony Brockwell, Joel Greenhouse, John Lehoczky, Heidi Sestrich, and Valerie Ventura.

The people at Addison-Wesley and other organizations that helped produce the book were Paul Anagnostopoulos, Patty Bergin, Dana Jones Bettez, Chris Cummings, Kathleen DeChavez, Alex Gay, Leah Goldberg, Karen Hartpence, and Christina Lepre.

If I left anyone out, it was unintentional, and I apologize. Errors inevitably arise in any project like this (meaning a project in which I am involved). For this reason, I shall post information about the book, including a list of corrections, on my Web page, https://www.stat.cmu.edu/~mark, as soon as the book is published. Readers are encouraged to send me any errors that they discover.

Mark J. Schervish

October 2020

Acknowledgments

There are many people that I want to thank for their help and encouragement during this revision. First and foremost, I want to thank Marilyn DeGroot and Morrie’s children for giving me the chance to revise Morrie’s masterpiece.

I am indebted to the many readers, reviewers, colleagues, staff, and people at Addison-Wesley whose help and comments have strengthened this edition. The reviewers were: