Course Introduction

• Prerequisite：Calculus, Probability Theory
• Recommended for： junior
• Introduction：

The origin of statistics can be traced back to the urge of governments to gather information about economic development and population. However, modern statistics is not only restricted to these two areas anymore, but also studies problems from psychology, medicin, anthropology, epigenetics, agriculture etc. Below, a more detailed description of the course is given.

• Syllabus：

1. Review of Probability Theory: probability space, probability measure, random variable, expectation, large sample theory
2. Function of Random Variables: distribution function, moment generating function, change of variables techniques
3. Theory of Sampling Distribution: order statistics, theory of sample mean and variance
4. Parameter Point Estimation: method of moment, maximum likelihood estimation, sufficiencyuniformly minimum variance estimation
5. Interval Estimation: confidence interval for poputation mean, variance, difference of means
6. Hypothesis Testing: most power test, uniformly most powerful tests, etc.

• Reference：

1. Hogg and Craig, Introduction to Mathematical Statistics
2. Mood, Graybill and Boes, Introduction to the Theory of Statistics