Introduction to Probability

Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider.

This edition demonstrates the applicability of probability to many human activities with examples and illustrations. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; special distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Law of Large Numbers; the Central Limit Theorem; and statistical inference. Each section provides relevant proofs, followed by exercises and useful hints. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site.

This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences.

Demonstrates the applicability of probability to many human activities with examples and illustrationsDiscusses probability theory in a mathematically rigorous, yet accessible wayEach section provides relevant proofs, and is followed by exercises and useful hintsAnswers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site

Preface
1. Some Motivating Examples
2. Some Fundamental Concepts
3. The Concept of Probability and Basic Results
4. Conditional Probability and Independence
5. Numerical Characteristics of a Random Variable
6. Some Special Distributions
7. Joint Probability Density Function of Two Random Variables and Related Quantities
8. Joint Moment Generating Function, Covariance and Correlation Coefficient of Two Random Variables
9. Some Generalizations to k Random Variables, and Three Multivariate Distributions
10. Independence of Random Variables and Some Applications
11. Transformation of Random Variables
12. Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results
13. An Overview of Statistical Inference
Appendix
Some Notation and Abbreviations
Answers to the Even-Numbered Exercises
Index