《Probability and Statistics A》Syllabus

Course Number:           2109030801

Course Name:               Probability Theory and Mathematical Statistics A

Instructors:          Li Man

Required Text:              Margo. Probability theory and mathematical statistics[M]. Beijing: Science Press, 2016.

Course Description:      Probability theory and mathematical statistics is a professional basic course for business administration, a course for studying the theory and method of random phenomena and their laws, and has a unique and irreplaceable role in the cultivation of high-quality talents. The content of this course includes: the basic concepts of probability theory, univariate and multivariate random variables and their distributions, numerical characteristics of random variables, statistics and sampling distributions, point estimation of parameters, etc. Through the study of this course, it provides a good mathematical tool for analyzing and studying random phenomena in real life.

                                                                                                   Credits/Teaching Hours

Outline of UG CPC Topics Covered in this Course:   (2Credits/32Teaching Hours)

Chapter 1 Random Events and Their Probabilities              8 Teaching Hours

Section 1 Random Events and Their Operations

Section 2 Probability of Random Events

Section 3 Classical and Geometric Generalizations

Section 4 Conditional Probability and Three Basic Formulas

Section 5 Independence of events and Bernoulli's generalization                     

Chapter 2 Random Variables and Their Distributions                       7 Teaching Hours

Section 1 Discrete Random Variables and Their Distribution Laws

Section 2 Distribution Functions of Random Variables

Section 3 Continuous Random Variables and Their Probability Densities

Section 4 Distribution of Random Variable Functions

Chapter 3 Multidimensional Random Variables and Their Distributions     

7 Teaching Hours

Section 1 Two-dimensional random variables and their distributions

Section 2 Two-dimensional discrete and continuous random variables

Section 3 Marginal Distribution

Section 4 Independence of Random Variables

Section 5 Distribution of Functions of Two-Dimensional Random Variables  

Chapter 4 Numerical Characteristics of Random Variables              6 Teaching Hours

Section 1 Mathematical Expectations

Section 2 Variance

Section 3 Covariance and Correlation Coefficients                                          

Chapter 5 Basic Knowledge of Mathematical Statistics                   2 Teaching Hours

Section 1 Population vs. Sample

Section 2 Statistics and Sampling Distribution

Chapter 6 Parameter Estimation                            2 Teaching Hours

Section 1 Moment Estimation Method for Parameters

Section 2 Maximum likelihood estimation of parameters

Total (Teaching Hours)                                                                 32  

Summary of UG CPC Topics Covered in this Course:              (32Teaching hours)