Probability Foundations for Engineers

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 a theorem or 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, such as events versus outcomes, so that they are more understandable. 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 is also useful to engineers already in the field who want to learn more about probability concepts. An updated solutions manual is available for qualified textbook adoptions. Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface to the Second Edition Author Chapter 1: Introduction 1.1 Historical Perspectives 1.2 Formal Systems 1.3 Intuition Exercises Chapter 2: A Brief Review of Set Theory 2.1 Introduction 2.2 Definitions 2.3 Set Operations 2.4 Venn Diagrams 2.5 Dimensionality 2.6 Conclusion Exercises Chapter 3: Probability Basics 3.1 Random Experiments, Outcomes and Events 3.2 Probability 3.3 Probability Axioms 3.4 Conditional Probability 3.5 Independence Exercises Chapter 4: Random Variables and Distributions 4.1 Random Variables 4.2 Distributions 4.2.1 Probability Mass Functions 4.2.2 Probability Density Functions 4.2.3 Survivor Functions 4.3 Discrete Distribution Functions 4.3.1 The Bernoulli Distribution 4.3.2 The Binomial Distribution 4.3.3 The Multinomial Distribution 4.3.4 The Hypergeometric Distribution 4.3.5 The Poisson Distribution 4.3.6 The Geometric Distribution 4.3.7 The Negative Binomial Distribution 4.4 Continuous Distribution Functions 4.4.1 The Exponential Distribution 4.4.2 The Gamma Distribution 4.4.3 The Weibull Distribution 4.4.4 The Beta Distribution 4.4.5 The Normal Distribution 4.4.6 The Lognormal Distribution 4.4.7 The Uniform Distribution 4.5 Conditional Probability 4.6 Residual Life Distributions 4.7 Hazard Functions 4.8 Mixture Distributions 4.9 Independent Random Variables Exercises Note Chapter 5: Joint, Marginal and Conditional Distributions 5.1 The Idea of Joint Random Variables 5.2 The Discrete Case 5.2.1 Marginal Probability Functions 5.2.2 Conditional Probability Functions 5.3 The Continuous Case 5.3.1 Marginal Probability Functions 5.3.2 Conditional Probability Functions 5.4 Independence 5.5 Bivariate and Multivariate Normal Distributions 5.6 Bivariate and Multivariate Exponential Distributions Exercises Chapter 6: Expectation and Functions of Random Variables 6.1 Expectation 6.2 Three Properties of Expectation 6.3 Expectation and Random Vectors 6.4 Conditional Expectation 6.5 General Functions of Random Variables 6.5.1 One-Dimensional Functions 6.5.2 Multidimensional Functions 6.6 Expectation and Functions of Multiple Random Variables 6.7 Sums of Independent Random Variables Exercises Chapter 7: Moment Generating Functions 7.1 Construction of the Moment Generating Function 7.2 Convolutions 7.3 Joint Moment Generating Functions 7.4 Conditional Moment Generating Functions Exercises Chapter 8: Approximations and Limiting Behavior 8.1 Distribution-Free Approximations 8.2 Normal and Poisson Approximations 8.3 Laws of Large Numbers and the Central Limit Theorem Exercises Index "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"-- "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 round out the updates for the new edition"-- Provided by publisher 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. It offers theory in an accessible manner and includes numerous practical examples based on engineering applications.