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Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton and Jay L. Devore
Publication Date: 
Number of Pages: 
Springer Texts in Statistics
[Reviewed by
Robert W. Hayden
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This book falls somewhere along the spectrum of texts for probability courses, mathematical statistics courses, and calculus-based statistics courses. In fact, the second author also wrote Probability and Statistics for Engineering and the Sciences, a text for a calculus-based statistics course. In terms of coverage, the first few chapters look very similar in the two books. After that the older book spends ten chapters on statistics while the newer book spends one. Rather than more statistics, we find chapters on Markov chains, random processes, and signal processing. A prerequisite of calculus of at least two variables (and a little matrix arithmetic for Markov chains) makes this unsuited to the lowest level probability course. At the other end, the small number of proofs in the exposition or exercises keeps it below the level of the more mathematical probability textbooks. Compared to a mathematical statistics textbook, it delves less deeply into the theory, and spends less time on statistical applications. All in all the title fairly represents this as suited to a mixed audience in the mathematical sciences.

One unusual feature of this text is the use of software. This is used not only for the obvious number crunching applications, but also, perhaps more importantly, for simulations, which are used both to get answers and to illustrate concepts. This part of the book is bilingual, using both R (a favorite of statisticians) and Matlab (a favorite of many engineers). Little effort is made to teach either programming language, but the programs in the text run about ten lines each and could easily be modified by students who might not be able to write them from scratch themselves. R is free and Matlab has a free clone called Octave so site licenses and student budgets should not be issues.

The exposition here has many examples and there are more than a thousand exercises. All are quite varied and interesting with applications from a wide variety of fields. The text is well-written with special attention to points that are often a source of confusion for students. Answers to odd-numbered exercises are provided.

This is an excellent textbook that should be considered by anyone offering or contemplating a course for which the level and topics covered are a good match. My only concern is that the single chapter on statistics might give some the idea that they have covered the equivalent of a good introductory statistics course. Imagine how you would react to the idea that a chapter in a biology textbook would substitute for a course in calculus.

After a few years in industry, Robert W. Hayden ( taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.


Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint probability distributions and their applications

The Basics of Statistical Inference

Markov chains

Random processes

Introduction to signal processing.