教學大綱 Syllabus

科目名稱：高等數理統計

Course Name: Advanced Mathematical Statistics

學年學期：114-1 Fall Semester, 2025
科目代碼：354001001 Course No.354001001

修別：必

Type of Credit: Required

3.0

學分數

Credit(s)

預收人數

Number of Students

課程資料Course Details

開課單位：統計碩一 Course Department:Statistics/M/1
授課老師：黃佳慧 Instructor: HUANG CHIA-HUI
先修科目：無Prerequisite(N/A)
上課時間：五234 Session: fri09-12

課程簡介Course Description

This course provides students with the principles of probability theory and the theory of statistical inference, such as estimation methods, confidence intervals, and hypothesis testing procedures.

Those topics are essential for graduate students for further development in the field of Statistics or related fields.

核心能力分析圖 Core Competence Analysis Chart

能力項目說明

課程目標與學習成效Course Objectives & Learning Outcomes

The students will be able to make theoretical derivations and works on the following topics:

1. Probability theory

2. Transformations and expectations, including moments and moment generating functions.

3. Common families of distributions, including discrete distributions, continuous distributions, exponential families, and location and scale families.

4. Multivariate random variables and their distributions

5. Properties of a random sample, including sampling from normal distribution, order statistics, convergence concepts, etc.

每周課程進度與作業要求 Course Schedule & Requirements

週次	課程主題	課程內容與指定閱讀	教學活動與作業
1	Probability theory	1.1-1.3	1.1: 1.1-1.3, 1.9, 1.10, 1.14 ; 1.2: 1.4-1.8, 1.11- 1.13, 1.15-1.32, 1.42, 1.43; 1.3: 1.33-1.41, 1.44
2	Random variables	1.4-1.6	1.4: 1.45, 1.46; 1.6: 1.47-1.55; 2.1: 2.1-2.10, 2.11(b), 2.12, 2.13, 2.22(a), 2.23(a)
3	CDF, moments	2.1-2.2	2.2: 2.11-2.16, 2.20-2.22, 2.23(b), 2.24 HW1(due on Week4)
4	MGF, distribution families	2.3-2.4	2.3: 2.28-2.38; 2.4: 2.4: 2.19, 2.39, 2.40 HW2(due on Week 6)
5	Common models	3.2-3.4	3.2: 3.1~3.15, 3.18, 3.19, 3.22(a)(b); 3.3: 3.17~3.21,3.22(c)(d)(e), 3.23-3.27
6	Local and scale families, inequalities	3.4-3.6	3.4: 3.28-3.35; 3.5: 3.36-3.43; 3.6: 3.44-3.50; HW3 (due on week 8)
7	Bivariate random variables	4.1	4.1: 4.1-4.7, 4.9, 4.14-4.16, 4.40(a)(b), 4.49
8	Review	Ch1-3	Review
9	Midterm	Ch1-3
10	Bivariate transformation, hierarchical and mixture models	4.2-4.4	4.2: 4.8, 4.10-4.13, 4.15-4.17, 4.40(c), 4.45, 4.48; 4.3: 4.19-4.29, 4.46, 4.47, 4.51; 4.4: 4.30-4.38
11	Multivariate distributions, covariance matrix	4.4-4.6	4.5: 4.40(d), 4.41-4.44, 4.50, 4.58, 4.59; 4.6: 4.51-4.56
12	Inequalities	4.6-4.7	4.6: 4.51-4.56 4.7: 4.62-4.65 HW4(due on week 14)
13	Random sample and its properties	5.1-5.2	5.1: 5.1, 5.2; 5.2: 5.3, 5.5-5.12
14	Sum of variables, generating a random sample	5.2; 5.6	5.2: 5.3, 5.5-5.12; 5.6: Exercise 5.45-5.50, 5.56
15	Sampling distribution, convergence properties	5.3;5.5	5.3: 5.12-5.20; 5.5: 5.29-5.44 HW5 (due on week 17)
16	Order statistics	5.4	5.4: 5.21-5.28
17	Review	4-5	Review
18	Final exam	4-5

授課方式Teaching Approach

90%

講述 Lecture

討論 Discussion

小組活動 Group activity

10%

數位學習 E-learning

其他： Others:

評量工具與策略、評分標準成效Evaluation Criteria

Attendance: 10%

HW: 25%

Midterm: 30%

Final: 35%

指定/參考書目Textbook & References

Statistical inference, second edution; George Casella and Roger L. Berger

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課程相關連結Course Related Links

課程附件Course Attachments

課程進行中，使用智慧型手機、平板等隨身設備 To Use Smart Devices During the Class

需經教師同意始得使用 Approval

教學大綱 Syllabus

科目名稱：高等數理統計

Course Name: Advanced Mathematical Statistics

修別：必

學分數

預收人數

課程簡介Course Description

核心能力分析圖 Core Competence Analysis Chart

課程目標與學習成效Course Objectives & Learning Outcomes

每周課程進度與作業要求 Course Schedule & Requirements

Probability theory

1.1-1.3

1.1: 1.1-1.3, 1.9, 1.10, 1.14 ; 1.2: 1.4-1.8, 1.11- 1.13, 1.15-1.32, 1.42, 1.43; 1.3: 1.33-1.41, 1.44

2

Random variables

1.4-1.6

1.4: 1.45, 1.46;

1.6: 1.47-1.55; 2.1: 2.1-2.10, 2.11(b), 2.12, 2.13, 2.22(a), 2.23(a)

3

CDF, moments

2.1-2.2

2.2: 2.11-2.16, 2.20-2.22, 2.23(b), 2.24

HW1(due on Week4)

4

MGF, distribution families

2.3-2.4

2.3: 2.28-2.38;

2.4: 2.4: 2.19, 2.39, 2.40

HW2(due on Week 6)

5

Common models

3.2-3.4

3.2: 3.1~3.15, 3.18, 3.19, 3.22(a)(b);

3.3: 3.17~3.21,3.22(c)(d)(e), 3.23-3.27

6

Local and scale families, inequalities

3.4-3.6

3.4: 3.28-3.35; 3.5: 3.36-3.43; 3.6: 3.44-3.50;

HW3 (due on week 8)

7

Bivariate random variables

4.1

4.1: 4.1-4.7, 4.9, 4.14-4.16, 4.40(a)(b), 4.49

8

Review

Ch1-3

Review

9

Midterm

Ch1-3

10

Bivariate transformation, hierarchical and mixture models

4.2-4.4

4.2: 4.8, 4.10-4.13, 4.15-4.17, 4.40(c), 4.45, 4.48; 4.3: 4.19-4.29, 4.46, 4.47, 4.51;

4.4: 4.30-4.38

11

Multivariate distributions, covariance matrix

4.4-4.6

4.5: 4.40(d), 4.41-4.44, 4.50, 4.58, 4.59; 4.6: 4.51-4.56

12

Inequalities

4.6-4.7

4.6: 4.51-4.56 4.7: 4.62-4.65

13

Random sample and its properties

5.1-5.2

5.1: 5.1, 5.2; 5.2: 5.3, 5.5-5.12

14

Sum of variables, generating a random sample

5.2; 5.6

5.2: 5.3, 5.5-5.12;

5.6: Exercise 5.45-5.50, 5.56

15

Sampling distribution, convergence properties

5.3;5.5

5.3: 5.12-5.20;

5.5: 5.29-5.44

HW5 (due on week 17)

16

Order statistics

1.1: 1.1-1.3, 1.9, 1.10, 1.14 ;
1.2: 1.4-1.8, 1.11- 1.13, 1.15-1.32, 1.42, 1.43;
1.3: 1.33-1.41, 1.44

1.6: 1.47-1.55;
2.1: 2.1-2.10, 2.11(b), 2.12, 2.13, 2.22(a), 2.23(a)

3.4: 3.28-3.35;
3.5: 3.36-3.43;
3.6: 3.44-3.50;

4.2: 4.8, 4.10-4.13, 4.15-4.17, 4.40(c), 4.45, 4.48;
4.3: 4.19-4.29, 4.46, 4.47, 4.51;

4.5: 4.40(d), 4.41-4.44, 4.50, 4.58, 4.59;
4.6: 4.51-4.56

4.6: 4.51-4.56
4.7: 4.62-4.65

5.1: 5.1, 5.2;
5.2: 5.3, 5.5-5.12

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