數理統計課程內容涵蓋相當的廣度與深度，讓學生能夠瞭解基本的理論統計概念，課程範圍包含：
1. 機率：排列組合、條件機率、貝氏定理、隨機變數、分布函數、期望值、條件期望值、動差
2. 機率分配計算方法：變數變換、動差母函數、摺積
3. 分布族：常見離散型與連續型分布，其特性及之間的關係
4. 位置族、尺度族、指數族
5. 聯合分佈、邊際分佈、條件分佈、條件期望值、共變異數、相關係數、混合分佈
6. 不等式：Chebyshev、Jensen、Hölder
7. 收歛概念與極限分配：順序統計量、機率收斂、分布收斂、中央極限定理、Delta方法
8. 點估計方法：MLE、method of moments
9. 點估計量性質：不偏性、一致性、有效性、充分性、完備性
10. 點估計評估準則：MSE、CRLB、MVUE、Rao-Blackwell
11. 區間估計方法與評估準則
12. 檢定方法：LRT
13. 檢定統計量評估準則: Neyman-Pearson Lemma, UMP test, MLR
14. 貝氏統計
The content of the mathematical statistic course covers a considerable level of diversity and depth, allowing students to understand the basic theoretical statistic concepts, and the course scope includes:
1. Chances: arrangement combination, conditional probability, Beth's theorem, random variables, distribution function, expectation value, conditional expectation value, difference
2. Calculation method of probability allocation: variable change, difference parent function, fold
3. Distribution family: Common dispersion and continuous distribution, their characteristics and relationships between them
4. Position family, scale family, index family
5. Joint distribution, side-by-side distribution, conditional distribution, conditional expectations, total variations, related numbers, mixed distribution
6. Inequality: Chebyshev, Jensen, Hölder
7. Concept of collection and extreme limit allocation: sequence statistics, probability limit, distribution limit, central extreme limit theorem, Delta method
8. Point estimation method: MLE, method of moments
9. Estimate the metrics: impartiality, consistency, effectiveness, adequacy, completion
10. Point-estimation evaluation criteria: MSE, CRLB, MVUE, Rao-Blackwell
11. Regional estimation method and evaluation criteria
12. Confirmation method: LRT
13. Confirmation metric evaluation criteria: Neyman-Pearson Lemma, UMP test, MLR
14. Bets Statistics
數理統計為統計理論的核心課程，課程主要教授統計理論與概念，為其他統計相關課程的理論基礎，並培養學生修習更高深與統計相關之課程的能力。修課學生應具備微積分的基礎。本課程藉由定義解析、定理推導與例題講解過程，學習機率論與統計推論的基本理論與概念。機率論課程內容包括機率基本概念與定義、分配、不等式、收歛概念與極限分配；統計推論課程內容包括點估計方法、區間估計方法、檢定方法等不同的方法與理論。
Mathematical statistics are the core course of the theory of the theory. The course mainly teaches the theory and concepts, is the theoretical foundation of other statistical-related courses, and cultivates students' ability to study higher-level and statistical-related courses. Course students should have a basic foundation for micro points. This course learns the basic theorems and concepts of probability theory and statistical recommendation through definitive analysis, theorem guidance and example explanation. The content of the chance discussion course includes the basic concepts and definitions of chance, allocation, inequality, collection concepts and extreme allocation; the content of the statistical recommendation course includes different methods and theoretical discussions such as point estimation methods, regional estimation methods, and confirmation methods.
1. George Casella and Roger L. Berger (2002) Statistical Inference (2/E), Duxbury Press.
2. R.V. Hogg, E.A. Tanis (2005) Probability and Statistical Inference (7/E), Prentice Hall.
3. Dennis Wackerly, William Mendenhall, Richard L. Scheaffer (2001) Mathematical Statistics with Applications (Mathematical Statistics) (6/E), Duxbury Press.
1. George Casella and Roger L. Berger (2002) Statistical Inference (2/E), Duxbury Press.
2. R.V. Hogg, E.A. Tanis (2005) Probability and Statistical Inference (7/E), Prentice Hall.
3. Dennis Wackerly, William Mendenhall, Richard L. Scheaffer (2001) Mathematical Statistics with Applications (Mathematical Statistics) (6/E), Duxbury Press.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| AssignmentsAssignments Assignments |
40 | |
| Midterm ExamMidterm Exam Midterm Exam |
30 | |
| Final ExamFinal Exam Final Exam |
30 |
