Course Description

This course is suitable for sophomoreof our university whose major is mathematics statistics or applied mathematics, and it is the antecedent courser of other subsequent selective courses provided by department of applied mathematics. Students are expected to have read and be familiar with advanced mathematics and linear algebra.The course is designed to equip students with a framework of probability, distribution functions of random variables (binomial, geometric, hypergeometric, exponential, gamma, normal and more), numerical characters，the law of large numbers,point estimation, interval estimation,hypothesis test, statistical distribution theory, asymptotic theory and so on. Understanding these mentioned above equips students for further studies in financial statistics, economics and so on.

Course Learning Outcomes

The student learning outcomes are what student would be able to know and understand of this course. In details are:

1. Understand meanings of probability, random variables or vectors, distribution functions, probability distribution functions, Independence and so on.

2. Be familiar with some kinds of distribution functions, such as binomial distribution, normal distribution, exponential distribution, uniform distribution, Poisson distribution, and be able to compute probability of some complex events using Total Probability Theorem and Bayes’ Rule.

3. Understand and compute Numerical Characters.

4. Understand the meaning of the law of large numbers

5. Understand binomial, geometric, hypergeometric, exponential, gamma, normal, T and F distributions and more.

6. Understand classic statistics theory including point estimation, interval estimation, hypothesis test, statistical distribution theory, asymptotic theory and so on.

Relationship to Other Courses

Pre-requisites: Advanced Mathematics, Linear Algebra

Textbook and Reading Lists

Textbook:

Shisong Mou, Yiming Cheng, Xiaolong Pu. Probability theory and mathematical statistics course. Higher Education Press, 2012.

Course Assessment

Item	Title	Due Date	Value
1	Task in home	Week 16	10%
2	Test and Questions in class	Randomly selected weeks	10%
3	Final exam	Exam period	80%

Course Schedule

Week	Topics	Text
1-2	Events and Probability + Random phenomena , Sample Space and Event + Classical Probability + Geometric Probability + Probability Space	Chapters 1
3-5	Conditional Probability and Statistical Independence: + Conditional Probability, Total Probability Theorem and Bayes’ Rule + Independence + Bernoulli Experiment, Random Walk + Binomial Distribution and Poisson Distribution	Chapters 2
6-7	Random Variable and Distribution Functions: + Random Variable and its Distribution Function + Random Vectors, Independence of Random Vectors + Functions of Random Variables	Chapters 3
8-10	Numerical Characters, Characteristic Function +Expectation, Variance, Moment, Correlation Coefficient + Characteristic Function Limit Theorem + the Law of Large Numbers + the Central Limit Theorem	Chapters 4
11-12	Statistic and its distribution + Population and sample + Statistics and Estimator + Sampling distribution + Order statistics + Sufficient statistic + Distribution family	Chapter 5
13-14	Point estimation: + moment estimation and consistent + MLE and asymptotic normality + UMVUE + C-R inequality + Linear estimator and BLUE	Chapter 6
15	Interval estimation: + Confidence interval + Confidence interval of normal parameters + large sample confidence interval	Chapter 7
16-17	Hypothesis test + Concept and procedure + Hypothesis test of normal mean + Hypothesis test difference between two normal mean + Inference of normal variance	Chapter 8