數理統計學（一）
開課教師｜Instructor
劉惠美
簡介 : 政大統計系教授
專長領域：線性不等式假設檢定、多變量分析、重點抽樣之應用、線性模型
課程介紹｜Content
This course is designed to cover some introductory theoretical knowledge of the
probability and statistics. Although the primary focus is on a mathematical
development of the subject, examples and exercises are oriented toward
applications. After taking this course, students can gain solid mathematical
understanding of probability theory fundamental to all future work in probability
and statistics.
課程目標｜Goal
Course Outline
1. Probability
2. Random Variables and Their Distributions
3. Some Special Distributions
4. Joint Distributions
5. Properties of Random Variables
6. Functions of Random Variables
7. Statistics and Sampling Distributions
修完此門課，可以考美國精算師考試的P(Probability)科。
課程進度｜Schedule
|
每週課程進度與作業要求Course Schedule & Requirements |
||||||
|
週次 Week |
日期 Date |
課程主題 Topic |
課程內容與指定閱讀Content and Reading Assignment |
教學活動與作業Teaching Activities and Homework |
助教任務 TA workload expectation |
|
|
課堂講授 In-class Hours |
課程前後 Outside-of-class Hours |
|||||
|
1 |
9/18 |
Probability |
請複習Chap 1. |
Chap.1, Exer 6,8,10,11,13 |
複習微積分 |
錄影及上傳上課內容 |
|
2 |
9/25 |
Random Variables and Their Distributions |
2.1~2.5 |
Chap. 1, Exer 18, 32, 57(c). Chap 2, Exer. 5,7,8 |
解題與複習第一週上課內容 |
錄影及上傳上課內容 |
|
3 |
9/26 |
補課(10/2 放假) Special Probability Distributions |
3.1~3.2 |
Chap. 2, Exer 24, 28, 29, 38, 40, 48. pop quiz |
解題與複習第二週上課內容 |
通知課務組借教室，錄影及上傳上課內容 |
|
4 |
10/09 |
NO Class |
3.3~3.4 |
Chap. 2 Exer. 53 Chap. 3, Exer. 8,9,19, 20 |
解題與複習第三週上課內容 |
錄影及上傳上課內容 |
|
5 |
10/16 |
Some Special Distributions |
4.1~ 4.3 |
Chap. 4, Exer. 1,2,3,4,6 |
解題與複習第四週上課內容 |
安排至電腦教室以R程式語言抽取隨機變數 |
|
6 |
10/23 |
Joint Distributions |
4.4~4.6 |
Chap. 4, Exer. 11,12,13,14,15 |
解題與複習第五週上課內容 |
錄影及上傳上課內容 |
|
7 |
10/30 |
Properties of Random Variables Quiz (I):老師命題 Quiz 1: 2.5-3.3 |
5.1~5.3 |
Quiz 1 3.4-5.4 or 5.5 Chap. 4, Exer. 16,17,18,20,22 Chap. 5, Exer. 1,2,3,4 |
監考及回答學生問題 |
協助閱卷 |
|
8 |
11/06 |
Properties of Random Variables |
5.4~5.5 |
Chap. 5, Exer. 10,11,12,13,19,31,34 發quiz考卷 |
講解quiz |
錄影及上傳上課內容 |
|
9 |
11/13 |
Midterm(2.5-5.3) |
GOOD LUCK |
no class |
監考及回答學生問題 |
協助閱卷 |
|
10 |
11/20 |
Functions of Random Variables |
6.1~6.4 |
Chap. 6, Exer. 1,3,4,8,9 發期中考考卷(預計) |
NO TA class |
錄影及上傳上課內容 |
|
11 |
11/27 |
Functions of Random Variables |
6.4~6.5 |
Chap. 6, Exer. 11,13,14,15 |
解題與複習第十週上課內容 |
錄影及上傳上課內容 |
|
12 |
12/04 |
Review Chap 6 |
7.1~7.3 |
Chap. 6, Exer. 16,17 |
解題與複習第十一週上課內容 |
錄影及上傳上課內容 |
|
13 |
12/11 |
Statistics and Sampling Distributions |
7.4~7.5 |
Chap. 7, Exer. 1,3,4. |
解題與複習第十二週上課內容 |
錄影及上傳上課內容 |
|
14 |
12/18 |
Statistics and Sampling Distributions |
7.6~7.7 |
(Quiz 3: 6.5-7.5) Chap. 7, Exer. 8,9,11 |
解題與複習第十三週上課內容 |
安排至電腦教室以R程式語言模擬中央極限定理 |
|
15 |
12/25 |
Statistics and Sampling Distributions Review Chap. 5-7 Quizz (II) |
7.6~7.7 Review Chap. 5-7 |
Chap. 7, Exer. 16,17 |
解題與複習第十四週上課內容 |
錄影及上傳上課內容 |
|
16 |
01/01 |
Holiday , No Class |
Study hard for final exam |
複習及練習解題多一小時office hour |
解題與複習第十五週上課內容，解題quizII |
錄影及上傳上課內容 |
|
17 |
01/08 |
Final Exam |
GOOD LUCK |
No TA Class |
監考及回答學生問題 |
協助閱卷 |
|
18 |
||||||
上課形式｜Activities
講述 90%
數位學習 10%
|
校內學員：94人 網路學員：17人 共111人 |
評分標準｜Grading
|
1.Homework (Assigned weekly) 2.TA Quizzes (biweekly) +TA Class attendance 20% 3.Mid-Term Exam：11/13/2020 09:10~12:00 30% 4.Quiz(I) + Quiz(II) 20% 5.Final Exam：1/08/2021 09:10~12:00 30% |
先備知識｜Prerequisites
微積分
參考書目｜Readings
Text Book：
Bain/Introduction to Probability and Mathematical Statistics (平裝) 2/E 1992
Reference：
1.Ghahramani, S. Fundamentals of Probability. Prentice-Hall, Inc., 1996.
2.Hogg, Robert V., and Craig, Allen T. Introduction to Mathematical Statistics. 5th edition, Prentice-Hall, Inc., 1995.
3.Hogg and Tanis, Probability and Statistical Inference. 6th edition, Prentice-Hall, Inc., 2001.
