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