The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for Instructors only), are available online at www.cambridge.org/9780521864701.
Reviewer: Charles Raymond Crawford
Engineers are finding more and more applications for probability and random processes as the technology they are asked to design and analyze becomes more complex. As a result, courses in this area at the senior and graduate levels are an important part of an engineering curriculum. In writing this text, the author's purpose, as stated in the introduction, is to show from "first principles" how probability theory can be used "to explain, model, analyze, and design technology developed by electrical and computer engineers." More specifically, he has organized the chapters so the text can be used in a first course in probability, which includes topics in random processes, as well as a second course that assumes some background in probability but concentrates on random processes. A little over half of the book covers probability, with the remainder of it being on random processes. The bibliography includes some journal articles but also standard texts on probability and random processes. The author has clearly tried to balance mathematical rigor and practical application. He does not follow a strict theorem/proof pattern, but tries to logically connect the definitions of concepts with results about them. He discusses probability, initially using finite set theory. He then uses this to motivate the definitions of probability, distribution, and expectation for the general case, while making some mention of complications for infinite sets. As another example, when the central limit theorem is presented, the derivation is delayed until the end of the section after discussions of some implications and applications of the theorem. The derivation of the theorem, at the end of the section, includes only enough detail to show the connection with Gaussian distribution, and the reader is referred to a standard reference for more information. With this organization, readers can choose to put more or less emphasis on the derivation, or even skip it altogether, without disrupting the flow of the text. Each chapter contains many examples and ends with several pages of exercises. Although many of the examples are from classic applications in electrical engineering, there are examples of applications to Web site and cellular phone traffic where the arrivals are assumed to have very general distributions. Unfortunately, in the final quarter of the text, which deals with Markov chains and long-term behavior, the applications are not discussed in much detail other than, for example, specifying that a process has a particular transition matrix. There is no example showing how a matrix might be determined from an application. Online Computing Reviews Service
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The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for Instructors only), are available online at www.cambridge.org/9780521864701.
'… stands alone as a textbook that encourages readers to work through and obtain working knowledge of probability and random processes.'
Source: IEEE Software
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