Probability Foundations for Engineers

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. "Suitable for a first course in probability theory, this textbook covers theory in an accessible manner and includes numerous practical examples based on engineering applications. The book begins with a summary of set theory and then introduces probability and its axioms. It covers conditional probability, independence, and approximations. An important aspect of the text is the fact that examples are not presented in terms of "balls in urns". Many examples do relate to gambling with coins, dice and cards but most are based on observable physical phenomena familiar to engineering students"-- "Preface This book is intended for undergraduate (probably sophomore-level) engineering students--principally industrial engineering students but also those in electrical and mechanical engineering who enroll in a first course in probability. It is specifically intended to present probability theory to them in an accessible manner. The book was first motivated by the persistent failure of students entering my random processes course to bring an understanding of basic probability with them from the prerequisite course. This motivation was reinforced by more recent success with the prerequisite course when it was organized in the manner used to construct this text. Essentially, everyone understands and deals with probability every day in their normal lives. There are innumerable examples of this. Nevertheless, for some reason, when engineering students who have good math skills are presented with the mathematics of probability theory, a disconnect occurs somewhere. It may not be fair to assert that the students arrived to the second course unprepared because of the previous emphasis on theorem-proof-type mathematical presentation, but the evidence seems support this view. In any case, in assembling this text, I have carefully avoided a theorem-proof type of presentation. All of the theory is included, but I have tried to present it in a conversational rather than a formal manner. I have relied heavily on the assumption that undergraduate engineering students have solid mastery of calculus. The math is not emphasized so much as it is used. Another point of stressed in the preparation of the text is that there are no balls-in-urns examples or problems. Gambling problems related to cards and dice are used, but balls in urns have been avoided"-- This textbook will continue to be the best suitable textbook written specifically for a first course on probability theory and designed for industrial engineering and operations management students. The book offers theory in an accessible manner and includes numerous practical examples based on engineering applications. Probability Foundations for Engineers, Second Edition continues to focus specifically on probability rather than probability and statistics. It offers a conversational presentation rather than theorem/proof and includes examples based on engineering applications as it highlights Excel computations. This new edition presents a review of set theory and updates all descriptions so they are more understandable such as events versus outcomes. Additional new material includes distributions such as beta and lognormal, a section on counting principles for defining probabilities, a section on mixture distributions, and a pair of distribution summary tables. Intended for undergraduate engineering students, this new edition textbook offers a foundational knowledge of probability. It can also be useful to engineers already in the field wanting to learn more about probability concepts. An updated solutions manual is available for qualified textbook adoptions. Front Cover Contents Preface Author Chapter 1: Introduction Chapter 2: A Brief Review of Set Theory Chapter 3: Probability Basics Chapter 4: Random Variables and Distributions Chapter 5: Joint, Marginal, and Conditional Distributions Chapter 6: Expectation and Functions of Random Variables Chapter 7: Moment-Generating Functions Chapter 8: Approximations and Limiting Behavior Appendix: Cumulative Poisson Probabilities Back Cover Suitable for a first course in probability theory and designed specifically for industrial engineering and operations management students, this book covers theory in an accessible manner and includes numerous practical examples based on engineering applications