Über die Autorin bzw. den Autor

JAMES L. JOHNSON holds a PhD in Mathematics and has twenty-five years experience in academic and industrial computer science. He is currently Professor of Computer Science at Western Washington University. He is also the author of Database: Models, Languages, Design.

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A unique probability study for computer science students

While many computer science curricula include only an introductory course on general probability, there is a recognized need for further study of this mathematical discipline within the specific context of computer science. Probability and Statistics for Computer Science develops introductory topics in probability with this particular emphasis, providing computer science students with an invaluable resource in their continued st udies and professional research.

James Johnson’s text begins with the basic definitions of probability distributions and random variables and then elaborates their properties and applications. Probability and Statistics for Computer Science treats the most common discrete and continuous distributions, showing how they find use in decision and estimation problems, and constructs computer algorithms for generating observations from the various distributions. This one-of-a-kind resource also:

• Includes a thorough and rigorous development of all the necessary supporting mathematics
• Provides an opportunity to reconnect applications with the theoretical concepts of distributions introduced in prerequisite courses
• Gathers supporting topics in an appendix: set theory, limit processes, real number structure, Riemann-Stieltjes integrals, matrix transformation, and determinants
• Uses computer science examples from computer science such as client-server performance evaluation and image processing

The author also addresses a variety of supporting topics, such as estimation arguments with limits, properties of power series, and Markov processes. Johnson’s text proves an ideal resource for computer science students and practitioners interested in a probability study specific to their field.

Aus dem Klappentext

A unique probability study for computer science students

While many computer science curricula include only an introductory course on general probability, there is a recognized need for further study of this mathematical discipline within the specific context of computer science. Probability and Statistics for Computer Science develops introductory topics in probability with this particular emphasis, providing computer science students with an invaluable resource in their continued st udies and professional research.

James Johnson’s text begins with the basic definitions of probability distributions and random variables and then elaborates their properties and applications. Probability and Statistics for Computer Science treats the most common discrete and continuous distributions, showing how they find use in decision and estimation problems, and constructs computer algorithms for generating observations from the various distributions. This one-of-a-kind resource also:

• Includes a thorough and rigorous development of all the necessary supporting mathematics
• Provides an opportunity to reconnect applications with the theoretical concepts of distributions introduced in prerequisite courses
• Gathers supporting topics in an appendix: set theory, limit processes, real number structure, Riemann-Stieltjes integrals, matrix transformation, and determinants
• Uses computer science examples from computer science such as client-server performance evaluation and image processing

The author also addresses a variety of supporting topics, such as estimation arguments with limits, properties of power series, and Markov processes. Johnson’s text proves an ideal resource for computer science students and practitioners interested in a probability study specific to their field.

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Probability and Statistics for Computer Science

By James L. Johnson

John Wiley & Sons

Copyright © 2003 James L. Johnson
All right reserved.
ISBN: 978-0-471-32672-4

Preface

This text develops introductory topics in probability and statistics with particular emphasis on concepts that arise in computer science. It starts with the basic definitions of probability distributions and random variables and elaborates their properties and applications. Statistics is the major application domain for probability theory and consequently merits mention in the title. Unsurprisingly, then, the text treats the most common discrete and continuous distributions and shows how they find use in decision and estimation problems. It also constructs computer algorithms for generating observations from the various distributions.

However, the text has a major subtheme. It develops in a thorough and rigorous fashion all the necessary supporting mathematics. This approach contrasts with that adopted by most probability and statistics texts, which for economy of space or for fear of mixing presentations of different mathematical sophistication, simply cite supporting results that cannot be proved in the context of the moment. With careful organization, however, it is possible to develop all the needed mathematics beyond differential and integral calculus and introductory matrix algebra, and this text purports to do just that.

Of course, as the book lengthens to accommodate the supporting mathematics, some material from the typical introduction to probability theory must be omitted. I feel the omissions are minor and that all major introductory topics receive adequate attention. Moreover, engagement with the underlying mathematics provides an opportunity to understand probability and statistics at a much deeper level than that afforded by mechanical application of unproved theorems.

Although the presentation is as rigorous as a pure mathematics text, computer science students comprise the book's primary audience. Certain aspects of most computer science curriculums involve probabilistic reasoning, such as algorithm analysis and performance modeling, and frequently students are not sufficiently prepared for these courses. While it is true that most computer science curriculums do require a course in probability and statistics, these courses often fail to provide the necessary depth. This text certainly does not fail in presenting a thorough grounding in elementary probability and statistics. Moreover, it seizes the opportunity to extend the student's command of mathematical analysis. This approach is different than that taken by other probability and statistics texts currently aimed at computer science curriculums. The more rigorous approach does require more work, both from the student and from the instructor, but the rewards are commensurate.

The engineering sciences, like computer science, also tend to use texts that place more emphasis on mechanical application of results than on the mathematical derivation of such results. Consequently, engineering science students will also benefit from the deeper presentation afforded by this text. Nevertheless, the primary audience remains computer science students because many of the illustrative examples are computer science applications. Therefore, from this point forward, I assume that I am addressing a computer science student or instructor.

Computer science students typically follow a traditional curriculum that includes one or two terms of probability and statistics, which follow prerequisite courses in differential and integral calculus and linear algebra. Although these prerequisite courses do introduce limit processes and matrix transformations, they typically emphasize formulas that isolate applications from the underlying theory. For example, if we drain a swimming pool with a sinusoidal cross-section, we can calculate how fast the water level falls without invoking limit operations. We simply set up a standard differential ratio and equate it to the drain flow rate. Why this works is buried in the theory and receives less and less emphasis once a satisfactory collection of calculation templates is available. This text provides an opportunity to reconnect with the theoretical concepts of these prerequisite courses. As it probes deeper into the properties of probability distributions, the text puts these concepts to fruitful use in constructing rigorous proofs.

The book's ambient prose deals with the principal themes and applications of probability, and a sequence of mathematical support modules interrupts this prose at strategic junctures. With some exceptions, these modules appear as needed by the probability concepts under discussion. A reader can omit the modules and still obtain a good grounding in elementary probability and statistics, including philosophical interpretations of probability and ample exercise in the associated numerical techniques. Reading the support modules will, however, strengthen this understanding and will also arouse an appreciation for the mathematics itself.

The encapsulation is as follows. An appendix gathers selected topics from set theory, limit processes, the structure of the real numbers, Riemann-Stieltjes integrals, matrix transformations, and determinants. The treatment first reviews the material at an introductory level. The prepared reader will be familiar with these concepts from previous courses, but the results are nevertheless proved in detail. The less prepared reader will certainly find frequent recourse to the appendix, and the text provides pointers to the appropriate sections. However, even the prepared reader will benefit from the introductory presentations, which serve both as a review of proof technique and as an introduction to the argument style pursued in the main text. Upon completing an introductory review, the appendix then extends the topics as necessary to support the arguments that appear in the main body of the text. Therefore, all chapters depend on the appendix for completeness. Even a reader well grounded in the aforementioned prerequisites can expect to spend some time mastering the specialized tools developed in the appendix.

The appendix, with its eclectic collection of review topics and specialized extensions, provides general mathematical background. There is need, however, for more specific supporting mathematics in connection with particular probabilistic and statistical concepts. Until perhaps halfway through the text, this supporting mathematics appears in mathematical interludes, which occur in each chapter. These interludes introduce particular results that are needed for the first time in that chapter. The first interlude deals with summation techniques, which are useful tools for the combinatoric problems associated with probability over equally likely outcomes. Others treat convergence issues in power series, stability features of Markov matrices, and sufficient statistics. Before taking up continuous distributions, however, it is appropriate to devote a full chapter to the mathematical issues that arise when one attempts to generalize discrete probability to uncountable sets and to the real line in particular. This chapter is actually a brief introduction to measure theory, and its logical place is just prior to the discussion of the common distributions on the real line. Two further interludes follow in subsequent chapters. They deal with limit theorems for continuous random variables and with decompositions of the sample variance. In short, the text exploits opportunities to introduce the mathematical analysis necessary to...