Probability Theory and Mathematical Statistics

Author: Ma Junying
Publisher:
Publish Date: 2004-09-01
Features: This book adheres to the principle of "few but essential, broad yet easy to understand" in its selection of materials. The content is closely aligned with the postgraduate entrance examination syllabus for mathematics, and the language and notation used in the text are standardized accordingly. The content is divided into two main parts: Probability and Mathematical Statistics.
Probability (Chapters 1-5) includes: Random events and probability, Random variables and their distributions, Multidimensional random variables and their distributions, Digital characteristics of random variables, Limit theorems.
Mathematical Statistics (Chapters 6-9) includes: Basic concepts of mathematical statistics, Parameter estimation, Hypothesis testing, Analysis of variance and preliminary regression analysis (Chapter 9 is optional based on professional needs).
In the presentation, the introduction of fundamental concepts is as intuitive as possible, using familiar real-world examples. The narrative is concise and clear, while the proofs and derivations are as rigorous as possible within the scope of advanced mathematics, with complex proofs appropriately simplified. However, the book provides clear explanations of how relevant knowledge can be applied to solve problems.
The book is rich in examples, with careful attention paid to the inclusion of application cases in engineering, economics, education, management, biology, and other fields. Each chapter is accompanied by a substantial number of exercises, some of which are comprehensive and challenging, suitable for practice by postgraduate entrance examination candidates. The question types include fill-in-the-blanks, multiple-choice, calculations, and proofs. The answers to all exercises are provided at the end of the book for reference.