Probability Theory and Mathematical Statistics
Date: 2018-10-24 Views: 16

Probability Theory and Mathematical Statistics

Course No.:  SMI1151304  Credit(s): 5

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 charactersthe 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.

Suggested reading lists:

XianPing Li. Basic of Probability Theory, 3rd edition. Beijing: People's Education Press, 2010 .

Sheldon M. Ross.  A first course in probability, 8th edition, Pearson Education Asia Ltd., 2010.

Shisong Mao, Xiaolin Lv. Mathematical Statistics. Beijing: RenminUniversity Press, 2011.

Xiru Chen. A Course on Mathematical Statistics, CSTU Press, 2009.

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