數理統計為統計系學生學習統計理論的核心課程，提供統計相關課程的理論根基，並且培養未來修習更高深統計相關課程的能力，課程內容涵概相當的廣度與深度，強調學生能夠了解基本的理論統計概念及在不同情況下的統計程序，課程主題包括統計推論，範圍包含：不偏性、一致性、有效性、指數族、充分性、最大概似估計量、最大概似法及其漸進理論、Cramér-Rao不等式、UMVUE、Rao-Blackwell定理、單一樣本與兩樣本之信賴區間及假設檢定的常態理論及其相關的大樣本方法、單一樣本與兩樣本之信賴區間及假設檢定的常態理論及其相關的大樣本方法、順序統計量、最適假設檢定、Neyman-Pearson引理、MP檢定、UMP檢定、MLR族、UMPU 檢定、LR檢定Mathematical statistics is the core course of students in the Department of Statistics to learn the theoretical foundation of the statistical related courses, and cultivate the ability to practice higher and deeper statistical related courses in the future. The course contents cover the similar diversity and depth, and emphasize that students can understand the basic theoretical concepts and the statistical procedures under different circumstances. The course topics include statistical recommendations, and the scope includes: impartiality, consistency, effectiveness, index family, sufficiency, maximum general similarity estimation, maximum general similarity method and its progressive theory. Comments, Cramér-Rao inequality, UMVUE, Rao-Blackwell theorem, the credibility area between single and two samples and the normal theory of hypothesis confirmation and its related large sample methods, the credibility area between single and two samples and the normal theory of hypothesis confirmation and its related large sample methods, sequence statistics, most suitable hypothesis confirmation, Neyman-Pearson lemma, MP confirmation, UMP confirmation, MLR family, UMPU Confirmation, LR confirmation
Hogg, R.V. and E.A. Tanis：Probability and Statistical Inference(8th Edition)
Hogg, R.V. and E.A. Tanis: probability and statistical inference(8TH edition)
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 第一次考試第一次考試 First exam |
20 | |
| 期中考期中考 Midterm exam |
25 | |
| 第二次考試第二次考試 Second exam |
25 | |
| 期末考期末考 Final exam |
30 |
