A4861 教學大綱表

教學大綱表 (102學年度第1學期)

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課程名稱 Course Title	(中文) 數理統計學(一) (英文) Mathematical Statistics			開課單位 Departments	應用數學系
				課程代碼 Course No.	A4861
授課教師 Instructor	張建瑋
學分數 Credit	3.0	必/選修 core required/optional	選修	開課年級 Level	大四
先修科目或先備能力(Course Pre-requisites)：A3810機率導論, A3820統計學
課程概述與目標(Course Overview and Goals)：This is a one-year course in mathematical statistics at the advanced undergraduate level. We will deal with probability and distribution theory as well as statistical inference. 1. Probability Space , Sigma-fields , and Limit of a Sequence of Events 2. Random Variables and Their Distributions 3. Moments and Probability Inequalities 4. Characteristic Functions , Moment Generating Functions , and Related Theorems 5. Stochastic Independence and Some Results 6. Basic Limit Theorems 7. Transformations of Random Vectors 8. Order Statistics and Related Theorems
教科書(Textbook)	Roussas (1997) A Course in Mathematical Statistics, 2nd edition, Academic Press.
參考教材(Reference)	Hogg, McKean, and Craig (2012) Introduction to Mathematical Statistics, 7th edition, Prentice Hall.

課程大綱 Syllabus			學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
序 No.	單元主題 Unit topic	內容綱要 Content summary	學生學習目標 Learning Objectives	單元學習活動 Learning Activities	學習成效評量 Evaluation	備註 Notes
1	Basic Concepts of Set Theory	Some Definitions and Notation Fields and sigma-Fields	Some Definitions and Notation Fields and sigma-Fields
2	Some Probabilistic Concepts and Results	Probability Function and Some Basic Properties and Results Conditional Probability Independence	Probability Function and Some Basic Properties and Results Conditional Probability Independence
3	Random Variables and Their Distributions	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution
4	Random Variables and Their Distributions	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution
5	Random Variables and Their Distributions	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution	Random Variables Cumulative Distribution Function Discrete and Continuous Random Variables Quantiles and Modes of a Distribution
6	Moments of Random Variables-Some Moment and Probability Inequality	Moment of Random Variables Expectations and Variances of Some R.V.'s Conditional Moments of Random Variables Some Important Applications: Probability and Moment Inequalities Convariance, Correlation Coefficient and Its Interpretation	Moment of Random Variables Expectations and Variances of Some R.V.'s Conditional Moments of Random Variables Some Important Applications: Probability and Moment Inequalities Convariance, Correlation Coefficient and Its Interpretation
7	Characteristic Functions, Moment Generating Functions and Related Theorems	1.Preliminaries 2.Definitions and Basic Theorems 3.The Characteristic Functions of Some Random Variables 4.The Moment Generating Function and Factorial Moment Generating Function of a Random Variable	1.Preliminaries 2.Definitions and Basic Theorems 3.The Characteristic Functions of Some Random Variables 4.The Moment Generating Function and Factorial Moment Generating Function of a Random Variable
8	Stochastic Independence with some Applications	Stochastic Independence: Criteria of Independence Some Consequences of Independence	Stochastic Independence: Criteria of Independence Some Consequences of Independence
9	Midterm	midterm	midterm
10	Basic Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems
11	Basic Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems
12	Basic Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems	Some Modes of Convergence Relationships Among the Various Modes of Convergence The Central Limit Theorem Laws of Large Numbers Further Limit Theorems
13	Transformations of Random Variables and Random Vectors	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables
14	Transformations of Random Variables and Random Vectors	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables
15	Transformations of Random Variables and Random Vectors	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables	The Univariate Case The Multivariate Case Linear Transformations of Random Vectors The Probability Integral Transform Conditional Distributions and Expectations The Correlation Coefficient Independent Random Variables
16	Order Statistics and Related Theorems	1.Order Statistics and Related Distributions 2.Further Distribution Theory: Probability of Converge of a Population Quantile	1.Order Statistics and Related Distributions 2.Further Distribution Theory: Probability of Converge of a Population Quantile
17	Order Statistics and Related Theorems	1.Order Statistics and Related Distributions 2.Further Distribution Theory: Probability of Converge of a Population Quantile	1.Order Statistics and Related Distributions 2.Further Distribution Theory: Probability of Converge of a Population Quantile
18	Final	Final	Final

教學要點概述：
1.自編教材 Handout by Instructor：
□ 1-1.簡報 Slids
□ 1-2.影音教材 Videos
□ 1-3.教具 Teaching Aids
□ 1-4.教科書 Textbook
□ 1-5.其他 Other
□ 2.自編評量工具/量表 Educational Assessment
□ 3.教科書作者提供 Textbook

成績考核 Performance Evaluation：期末考：30% 期中考：30% 平時考：40%

教學資源(Teaching Resources)：
□ 教材電子檔(Soft Copy of the Handout or the Textbook)
□ 課程網站(Website)
課程網站(Website)：http://elearn.ttu.edu.tw/learn/index.php
扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php