Probability and statistics

Course Code: B13003Y

Course Name: Probability and Statistics

Credits: 4.0

Pre-requisite: Calculus and Algebra

Lecture Time: 20 weeks, 2 sessions/week, 2 hours/session

Instructors:Null

Course Description

This course is designed as a required course for undergraduate students with major in math and physics. Students can learn the basic theoretical knowledge and statistical analysis methods, which lay foundation for related research and applications.

Topics and Schedule

1.            Probability of events

1.1.   What is probability?

1.2.   The computation of classic probability

1.3.   The computation of events, conditional probability and indepence

1.4.   Total probability formula and bayes’ formula

2.            Random variables and probability distribution

2.1.   One dimensional random variable

2.2.   Multi dimensional random variable

2.3.   Conditional probability distribution and independence of random variables

2.4.   The probability distribution of function of random variables

3.            Numeric characteristics of random variables

3.1.   Expected value and medium

3.2.   Variance and moment

3.3.   Covariance and correlation coefficient

3.4.   Law of large numbers and central limit theorem

4.            Parameter estimation

4.1.   Basic definition of statistics

4.2.   Moment estimation, Maximum likelihood estimation and Bayes estimation

4.3.   Rules for point estimation

4.4.   Set estimation

5.            Hypothesis testing

5.1.   Definition

5.2.   Some important parameter testing

5.3.   Goodness of fit testing

6.            Regression analysis and variance analysis

5.1.   Definition of regression analysis

5.2.   One variable linear regression

5.3.   Two variables linear regression

5.4.   Logistic regression

5.5.   Variance analysis

The grades include midterm examination, final examination and the completion of weekly homework.

Textbook

Xiru Chen et al., Probability and Statistics, University of Science and Technology of China Press, 2009

References

[1] Jiading Chen and Zhongguo Zheng, Probability and Statistics, Beijing university Press, 2007

Course Website

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