數理統計學(一)

劉惠美
統計學系
2020/09/01
~ 2021/01/31
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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.

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