Probability Theory and Mathematical Statistics

Author: Ge Yubo
Publisher:
Publish Date: 2005-04-01
Features: This book is written based on the teaching requirements for the "Probability Theory and Mathematical Statistics" course for non-university mathematics majors, as well as the author's decades of teaching experience and accumulation at Tsinghua University. The probability theory section includes: probability and conditional probability, models with equally likely outcomes, independence of events; basic concepts of random variables, random vectors, and distributions; the generation, properties, and relationships of important distribution laws, as well as the distribution of functions of random vectors (including variables); mathematical expectation, moments, variance, covariance between two random variables, and correlation coefficients; major limit theorems, conclusions, and applications. The mathematical statistics section includes: the concepts of population and sample, sampling distributions and statistics; parameter estimation (point estimation, interval estimation, and criteria for good estimators); hypothesis testing for parameters of normal and non-normal populations, testing for differences in parameters between two independent normal populations, and non-parametric tests (distribution fitting and rank sum tests); linear regression analysis. This book can be used as a textbook for non-mathematics majors in higher education institutions and mathematics majors in ordinary normal universities, as well as a reference book for engineering and technical personnel.