Probability. Robert P. Dobrow

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PREFACE

      Probability: With Applications and R is a probability textbook for undergraduates. The second edition contains modest changes from the first, including some reorganization of material. It assumes knowledge of differential and integral calculus (two semesters of calculus, rather than three semesters). Double integrals are introduced to work with joint distributions in the continuous case, with instruction in working with them provided in an appendix. While the material in this book stands on its own as a “terminal” course, it also prepares students planning to take upper level courses in statistics, stochastic processes, and actuarial sciences.

      There are several excellent probability textbooks available at the undergraduate level, and we are indebted to many, starting with the classic Introduction to Probability Theory and Its Applications by William Feller.

      Our approach is tailored to our students and based on the experience of teaching probability at a liberal arts college. Our students are not only math majors but come from disciplines throughout the natural and social sciences, especially biology, physics, computer science, and economics. Sometimes we will even get a philosophy, English, or arts history major. They tend to be sophomores and juniors. These students love to see connections with “real-life” problems, with applications that are “cool” and compelling. They are fairly computer literate. Their mathematical coursework may not be extensive, but they like problem solving and they respond well to the many games, simulations, paradoxes, and challenges that the subject offers.

Several features of our textbook set it apart from others. First is the emphasis on simulation. We find that the use of simulation, both with “hands-on” activities in the classroom and with the computer, is an invaluable tool for teaching probability. We use the free software R and provide supplemental resources (on the text website) for getting students up to speed in using and understanding the language. We recommend that students work through the introductory R supplement, and encourage use of the other supplements that enhance the code and discussion from the textbook with additional practice. The book is not meant to be an instruction manual in R; we do not teach programming. But the book does have numerous examples where a theoretical concept or exact calculation is reinforced by a computer simulation. The R language offers simple commands for generating samples from probability distributions. The book references numerous R script files, that are available for download, and are contained in the R supplements, also available for download from the text website. It also includes many short R “one-liners” that are easily shown in the classroom and that students can quickly and easily duplicate on their computer. Throughout the book are numerous “R” display boxes that contain these code and scripts. Students and instructors may use the supplements and scripts to run the book code without having to retype it themselves. The supplements also include more detail on some examples and questions for further practice.

      In addition to simulation, another emphasis of the book is on applications. We try to motivate the use of probability throughout the sciences and find examples from subjects as diverse as homelessness, genetics, meteorology, and cryptography. At the same time, the book does not forget its roots, and there are many classical chestnuts like the problem of points, Buffon's needle, coupon collecting, and Montmort's problem of coincidences. Within the context of the examples, when male and female are referred to (such as in the example on colorblindness affecting males more than females), we note that this refers to biological sex, not gender identity. As such, we use the term “sex” not “gender” in the text.

      Following is a synopsis of the book's 11 chapters.