Probability Theory

This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author's 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory.

Contents:

Probabilities

Conditional Probabilities and Independence

Random Variables and Their Distribution

Operations on Random Variables

Expected Value, Variance, and Covariance

Normally Distributed Random Vectors

Limit Theorems

Introduction to Stochastic Processes

Mathematical Statistics

Appendix

Bibliography

Index