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.
Author(s): Joel A. Nachlas
Edition: 2
Publisher: CRC Press
Year: 2023
Language: English
Pages: 185
City: Boca Raton
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
