Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Spring Semester
Year 2026 355038 Probability 1 3.0 3 ▲ Chun-Ling Lin 4EN2A 76 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	355038	Probability	1	3.0	3	▲	Chun-Ling Lin	4EN2A	76	0

Course Plan：

Instructor Chun-Ling Lin　Office Hours

Email ginnylin@ntut.edu.tw

Last Updated 2025-12-11 09:05:53

Course Objective 本課程介紹機率學的基本概念與應用，包括集合、排列組合、機率理論、條件機率、隨機變數、累積分佈函數、期望值與變異數等內容。課程涵蓋離散型與連續型機率分配、聯合分配、隨機變數的函數變換，以及順序統計量與基礎統計量的介紹。此外，學生將學習柴比雪夫不等式、大數定律與中央極限定理等重要定理，並透過期中考試與期末考試進行學習評估。This course introduces fundamental concepts and applications of probability, including sets, permutations and combinations, probability theory, conditional probability, random variables, cumulative distribution functions, and measures such as expectations and variances. The course covers discrete and continuous probability distributions, joint distributions, transformations of random variables, order statistics, and basic statistical measures. Additionally, students will study Chebyshev’s inequality, the law of large numbers, and the central limit theorem, with learning progress assessed through midterm and final examinations.

Course Schedule 第1週集合與排列組合 Sets, Permutations, and Combinations 第2週機率概論與條件機率 Introduction to Probability and Conditional Probability 第3週條件機率與獨立性，隨機變數的概念 Conditional Probability, Independence, and Random Variables 第4週隨機變數與累積分佈函數 Random Variables and Cumulative Distribution Functions 第5週期望值、變異數與動差生成函數 Expectation, Variance, and Moment Generating Functions 第6週特徵函數與隨機變數的函數變換 Characteristic Functions and Transformations of Random Variables 第7週離散型機率分配 (Part 1) Discrete Probability Distributions (Part 1) 第8週離散型機率分配 (Part 2) Discrete Probability Distributions (Part 2) 第9週期中考試 Midterm Exam 第10週連續型機率分配 (Part 1) Continuous Probability Distributions (Part 1) 第11週連續型機率分配 (Part 2) Continuous Probability Distributions (Part 2) 第12週聯合機率分配與條件分配 Joint Probability Distributions and Conditional Distributions 第13週期望值的性質 Properties of Expectation 第14週期望值性質與二元常態分配 Properties of Expectation and Bivariate Normal Distribution 第15週二維隨機變數的函數變換 Transformations of Bivariate Random Variables 第16週順序統計量與基本統計量 Order Statistics and Basic Statistical Measures 第17週柴比雪夫不等式、大數定律與中央極限定理 Chebyshev's Inequality, Law of Large Numbers, and Central Limit Theorem 第18週期末考試 Final Exam

Evaluation and grading policy 40% Attendance rate + Homework 30% Midterm exam 30% Final exam

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:No
機率學作者：姚賀騰出版社：全華圖書出版日期：2019/09/04 語言：繁體中文

The access to curricular consultation 學生可在Office Hours 時間至綜合科館 312-2 辦公室進行面對面討論，或透過電子郵件聯繫進行課程相關諮詢，信箱為：ginnylin@ntut.edu.tw。

Expanding teaching and resources

The course corresponds to the SDGs SDG4：優質教育（Quality Education）

Does the course incorporate AI ● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process）

Note
　

Instructor	Chun-Ling Lin　Office Hours
Email	ginnylin@ntut.edu.tw
Last Updated	2025-12-11 09:05:53
Course Objective	本課程介紹機率學的基本概念與應用，包括集合、排列組合、機率理論、條件機率、隨機變數、累積分佈函數、期望值與變異數等內容。課程涵蓋離散型與連續型機率分配、聯合分配、隨機變數的函數變換，以及順序統計量與基礎統計量的介紹。此外，學生將學習柴比雪夫不等式、大數定律與中央極限定理等重要定理，並透過期中考試與期末考試進行學習評估。This course introduces fundamental concepts and applications of probability, including sets, permutations and combinations, probability theory, conditional probability, random variables, cumulative distribution functions, and measures such as expectations and variances. The course covers discrete and continuous probability distributions, joint distributions, transformations of random variables, order statistics, and basic statistical measures. Additionally, students will study Chebyshev’s inequality, the law of large numbers, and the central limit theorem, with learning progress assessed through midterm and final examinations.
Course Schedule	第1週集合與排列組合 Sets, Permutations, and Combinations 第2週機率概論與條件機率 Introduction to Probability and Conditional Probability 第3週條件機率與獨立性，隨機變數的概念 Conditional Probability, Independence, and Random Variables 第4週隨機變數與累積分佈函數 Random Variables and Cumulative Distribution Functions 第5週期望值、變異數與動差生成函數 Expectation, Variance, and Moment Generating Functions 第6週特徵函數與隨機變數的函數變換 Characteristic Functions and Transformations of Random Variables 第7週離散型機率分配 (Part 1) Discrete Probability Distributions (Part 1) 第8週離散型機率分配 (Part 2) Discrete Probability Distributions (Part 2) 第9週期中考試 Midterm Exam 第10週連續型機率分配 (Part 1) Continuous Probability Distributions (Part 1) 第11週連續型機率分配 (Part 2) Continuous Probability Distributions (Part 2) 第12週聯合機率分配與條件分配 Joint Probability Distributions and Conditional Distributions 第13週期望值的性質 Properties of Expectation 第14週期望值性質與二元常態分配 Properties of Expectation and Bivariate Normal Distribution 第15週二維隨機變數的函數變換 Transformations of Bivariate Random Variables 第16週順序統計量與基本統計量 Order Statistics and Basic Statistical Measures 第17週柴比雪夫不等式、大數定律與中央極限定理 Chebyshev's Inequality, Law of Large Numbers, and Central Limit Theorem 第18週期末考試 Final Exam
Evaluation and grading policy	40% Attendance rate + Homework 30% Midterm exam 30% Final exam
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:No 機率學作者：姚賀騰出版社：全華圖書出版日期：2019/09/04 語言：繁體中文
The access to curricular consultation	學生可在Office Hours 時間至綜合科館 312-2 辦公室進行面對面討論，或透過電子郵件聯繫進行課程相關諮詢，信箱為：ginnylin@ntut.edu.tw。
Expanding teaching and resources
The course corresponds to the SDGs	SDG4：優質教育（Quality Education）
Does the course incorporate AI	● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process）
Note