If you want to make scientific decisions based on a big amount of stochastic data processing, you need to master some important tools for quantitative analysis of random phenomena. Probability theory and mathematical statistics is a mathematical discipline, focused on studing the statistical law of random phenomena, which has been widely applied to economic, society, management, finance, biology, environment, transportation and other fields. Therefore, probability theory and mathematical statistics is not only an important basic common course in college, but also a practical and highly applied subject for whose is major in statistics and mathematics. In the mathematical modeling contest for college students such as MCM/ICM, statistics is also the basic contest to support data analysis.
This course is for undergraduate student, and you can start to study this course as long as you know the elementary calculus.
Lecture 1: Random Events and Probability
Curriculum Development Overview and Three Elements of Probability
Total Probability Formula
Independence and Application of Events
Classical Probability
Bayesian Formula
Geometric Probability
Conditional Probability and Multiplication Formula
Lecture 2 One-Dimensional Random Variables and Their Distribution
Uniform Distribution and Exponential Distribution
The Distribution of A Class of Discrete Random Variables
Poisson Distribution and Poisson Theorem
Distribution of Continuous Random Variable Functions
Random Variables and Their Distribution
Normal Distribution
Lecture 3: Multidimensional Random Variables and Their Distribution
Multidimensional Random Variables and Distribution (1)
Distribution of Maximum and Minimum Values of Random Variables
The Marginal distribution law and the marginal density function
Multidimensional Random Variables and Distribution (2)
Distribution of Summation of Random Variables
Conditional Distribution and Independence of Random Variables
Find Distribution with Combination Method of Function and Image
Lecture 4: Numerical Characteristics of Random Variables
Application of Mathematical Expectation and Variance
Standardization and Correlation Coefficient
The Linear Property and Application of Mathematical Expectation
The Property of Variance and Covariance
Definition of Mathematical Expectation and Variance
Lecture 5: Limit Theorem
Central Limit Theorem
Law of Large Numbers
Lecture 6: Basic Concepts of Mathematical Statistics
Distribution of Sample Mean Statistics
Distribution of Sample Variance Statistics
Basic Concepts of Mathematical Statistics
Lecture 7: Parameter Estimation
What Is Parameter Estimation
Maximum Likelihood Estimation for Continuous Distribution
Likelihood Principle and Likelihood Function
Confidence Interval Estimation
Maximum Likelihood Estimation for A General Discrete Distribution
Moment Estimation
Lecture 8: Hypothesis Testing
Test for the Variance of Normal Population
The Basic Principle of Hypothesis Testing
Chi-Square Test of Goodness Fitting
Test for the Mean of Normal Population
Two Types of Errors
Lecture 9: Regression Analysis
Unary Linear Regression: Correlation Coefficient Test
Unary Linear Regression: Least Squares Estimation
Rong, Tengzhong, Liu, Qiongsun et al., Probability and Mathematical Statistics (Second Edition) [M], Higher Education Press, 2018.6(Chinese)
Mao, Shisong, Cheng, Yiming, Pu, Xiaolong. Probability Theory and Mathematical Statistics Course [M], Higher Education Press, 2011.2.(Chinese)
Probability and Statistical Inference, 8th Edition, Robert V. Hogg, Elliot Tanis, Pearson, 2010
1. How much does it cost to join this course to study?
It is totally free.
2. Can I still join this course after it has began?
You can register at any time, but you will not get the corresponding score when you submit your assignment after the deadline.
3. What is the composition of the grade in this course?
The final score will be composed by three parts: Quiz test 50%, Course discussion 10% (meaningless message will be record 0), Final examination 40%.