Probability Foundations for Engineers (Hardback) book cover

Probability Foundations for Engineers

By Joel A. Nachlas

© 2012 – CRC Press

184 pages | 9 B/W Illus.

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Hardback: 9781466502994
pub: 2012-05-09
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About the Book

Suitable for a first course in probability theory and designed specifically for industrial engineering and operations management students, Probability Foundations for Engineers covers theory in an accessible manner and includes numerous practical examples based on engineering applications. Essentially, everyone understands and deals with probability every day in their normal lives. Nevertheless, for some reason, when engineering students who have good math skills are presented with the mathematics of probability theory, there is a disconnect somewhere.

The book begins with a summary of set theory and then introduces probability and its axioms. The author has carefully avoided a theorem-proof type of presentation. He includes all of the theory but presents it in a conversational rather than formal manner, while relying on the assumption that undergraduate engineering students have a solid mastery of calculus. He explains mathematical theory by demonstrating how it is used with examples based on engineering applications. An important aspect of the text is the fact that examples are not presented in terms of "balls in urns". Many examples relate to gambling with coins, dice and cards but most are based on observable physical phenomena familiar to engineering students.


… responds to a need that I felt some years ago, which is to provide a basic and direct presentation of probability to engineers.

— Enrico Zio, Politecnico di Milano, Dipartimento Energia, Milano Italy

I think this will make an excellent introductory book on probability for engineers and it will prepare the IE, CE and EE students for advanced courses that deal with random processes.

— Edward A. Pohl, University of Arkansas, Fayetteville, USA

The theories are presented in a conversational rather than formal form as in most of the literature on probability. … introduces the reader in the field of randomness in a nice way. It gives a good starting point for more advanced studies. … creates a solid foundation to build up knowledge in more advanced statistical research. … The strength of the book is that it presents and translates the intuition concerning probability into mathematical structures using examples and explanations rather than traditional approach of theorem and proof. … perfect for undergraduate engineering students looking for a text book on probability.

— Prof. Uday Kumar, Luleå University of Technology, Sweden

One of the distinctive feature (and one of its strength) of the book "probability foundations for engineers" is that it gives an in-depth and rigorous presentation of probability theory, while avoiding a classical mathematical – Theorems/Proofs- presentation. … As the author himself writes, he wants his book to be a supporting tool to go from intuition to mathematical rigor and this is certainly rewarding and fruitful from the pedagogical point of view. … The Approach of using everyday engineering intuition to introduce the basic notions of probabilities theory should make this book a valuable tool for engineering students who wants to learn the basic concepts and notions of probability theory and to be able to make use of these on engineering problems.

— Christophe Bereguer, Grenoble Institute of Technology, France

… this book takes a fresh approach to teaching undergraduate engineering students the fundamentals of probability. The book exploits students’ existing intuition regarding probabilistic concepts when presenting these concepts in a more rigorous manner. Students should be better able to retain the knowledge gained through reading this text because of the relevance of the examples and applications.

Lisa Maillart, University of Pittsburgh, Pennsylvania, USA

Table of Contents

Historical Perspectives

Formal Systems



A Brief Review of Set Theory



Set Operations

Venn Diagrams




Probability Basics

Random Experiments, Outcomes, and Events


Probability Axioms

Conditional Probability



Random Variables and Distributions

Random Variables


Discrete Distribution Functions

Continuous Distribution Functions

Conditional Probability

Hazard Functions

Independent Random Variables


Joint, Marginal, and Conditional Distributions

The Idea of Joint Random Variables

The Discrete Case

The Continuous Case


Bivariate and Multivariate Normal Distributions


Expectation and Functions of Random Variables


Three Properties of Expectation

Expectation and Random Vectors

Conditional Expectation

General Functions of Random Variables

Expectation and Functions of Multiple Random Variables

Sums of Independent Random Variables


Moment-Generating Functions

Construction of the Moment-Generating Function


Joint Moment-Generating Functions

Conditional Moment-Generating Functions


Approximations and Limiting Behavior

Distribution-Free Approximations

Normal and Poisson Approximations

Laws of Large Numbers and the Central Limit Theorem


Appendix: Cumulative Poisson Probabilities


Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
MATHEMATICS / Probability & Statistics / Bayesian Analysis
TECHNOLOGY & ENGINEERING / Operations Research