Probability Foundations for Engineers

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