Probability Foundations for Engineers (Hardcover)

Historical Perspectives
Formal Systems
Intuition
Exercises

A Brief Review of Set Theory
Introduction
Definitions
Set Operations
Venn Diagrams
Dimensionality
Conclusion
Exercises

Probability Basics
Random Experiments, Outcomes, and Events
Probability
Probability Axioms
Conditional Probability
Independence
Exercises

Random Variables and Distributions
Random Variables
Distributions
Discrete Distribution Functions
Continuous Distribution Functions
Conditional Probability
Hazard Functions
Independent Random Variables
Exercises

Joint, Marginal, and Conditional Distributions
The Idea of Joint Random Variables
The Discrete Case
The Continuous Case
Independence
Bivariate and Multivariate Normal Distributions
Exercises

Expectation and Functions of Random Variables
Expectation
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
Exercises

Moment-Generating Functions
Construction of the Moment-Generating Function
Convolutions
Joint Moment-Generating Functions
Conditional Moment-Generating Functions
Exercises

Approximations and Limiting Behavior
Distribution-Free Approximations
Normal and Poisson Approximations
Laws of Large Numbers and the Central Limit Theorem
Exercises

Appendix: Cumulative Poisson Probabilities
Index