Undergraduate Mathematics Textbook Probability Theory

Author: He Shuyuan
Publisher:
Publish Date: 2006-01-01
Features: This book is a textbook for the foundational course "Probability Theory" in higher education institutions. The book is divided into six chapters, covering topics such as classical probability models and probability spaces, random variables and probability distributions, random vectors and their distributions, mathematical expectation and variance, characteristic functions and probability limit theorems, and an introduction to stochastic processes. Each section is accompanied by exercises, and each chapter includes a comprehensive set of review problems. At the end of the book, answers or hints to the exercises are provided for reference. The book offers a systematic and comprehensive introduction to the fundamental concepts of probability theory, incorporating many concise and innovative explanations that help readers better understand the material and delve deeper into the essence of the problems. The book is written with rigorous reasoning, detailed derivations, and abundant examples. The selected examples reflect real-life scenarios, such as gambling problems, court cases, corruption among officials, cultural heritage preservation, genetic models, collection problems, sensitive issue surveys, and medical efficacy issues. The book presents a powerful method for solving complex problems by discussing the densities of functions of computer-generated random variables and random vectors. When discussing multivariate normal distributions, it introduces degenerate multivariate normal distributions. In the section on mathematical expectation, it provides the expectation of mixed distributions. The central limit theorem is explained with its background and applications. This book can serve as a textbook or teaching reference for undergraduate students in comprehensive universities, normal universities, science and engineering universities, and finance and economics universities taking the "Probability Theory" course. The prerequisite for studying this book is advanced mathematics.