國立中興大學教學大綱

課程名稱	(中) 機率論(2260)
	(Eng.) Introduction to Probability
開課單位	應數系
課程類別	必修	學分	3	授課教師	沈宗荏
選課單位	應數系 / 學士班	授課使用語言	英文	開課學期	1142
課程簡述	This course introduces the core concepts and analytical tools of probability theory that underpin modern statistics and data analysis. Starting from set notation and probability set functions, the course develops conditional probability and independence, then moves to random variables, distribution functions, expectation, moment generating functions, and foundational inequalities. Building on these ideas, students will study multivariate distributions, including marginal and conditional distributions, conditional expectation and variance, independence and correlation, and distributional transformations (including the Jacobian method). The course concludes with major discrete and continuous distribution families, such as binomial, Poisson, gamma, and chi-square distributions, and selected additional continuous models. Taught in English (EMI), the course emphasizes precise probabilistic reasoning, clear mathematical communication, and problem solving skills that prepare students for subsequent study in Mathematical Statistics (I) and (II).
先修課程名稱

課程與核心能力關聯配比(%)

課程目標之教學方法與評量方法

課程目標

核心能力

配比(%)

教學方法

評量方法

By the end of this course, students will be able to:

① Use the language of probability correctly by applying set operations, probability axioms, and probability set functions to represent and analyze events.

② Compute and interpret conditional probability and independence, and use these concepts to structure probabilistic arguments and solve multi-stage problems.

③ Work fluently with random variables and distributions by deriving and interpreting cumulative distribution functions and related probability statements.

④ Calculate and apply expectations and moments, including moment generating functions, to obtain means, variances, and other special expectations.

⑤ Apply key probabilistic inequalities to bound probabilities and to support rigorous reasoning about random variation.

⑥ Analyze multivariate distributions by deriving marginal and conditional distributions, and by computing conditional expectation and conditional variance.

⑦ Quantify dependence between random variables using independence concepts and correlation coefficients, and interpret the implications for modeling.

⑧ Perform distributional transformations for functions of random variables, including multivariate transformations using the Jacobian technique.

⑨ Recognize, derive, and use major distribution families (binomial, Poisson, gamma, chi-square, and selected additional continuous distributions) and explain when each model is appropriate.

⑩ Communicate probabilistic reasoning in English (EMI) using standard terminology and notation, presenting solutions in a clear, logically structured manner suitable for further study in Mathematical Statistics (I) and (II).

3.統計分析專業知識

6.數學、統計、力學之理論解析

講授

討論

其他

測驗

作業

出席狀況

書面報告

授課內容(單元名稱與內容、習作/每週授課、考試進度-共16週加自主學習)

週次	授課內容
第1週	Chapter 1. Probability and Distribution Topics: Review of Set Notations; Probability Set Functions
第2週	Chapter 1. Probability and Distribution Topic: Conditional Probability and Independence ‼️3/5 (Thursday) I will invite Professor Takeshi Emura of Hiroshima University, Japan, to deliver a talk for this class.
第3週	Chapter 1. Probability and Distribution Topics: Random Variables; Cumulative Distribution Functions
第4週	Chapter 1. Probability and Distribution Topics: Expectation of a Random Variable; Some Special Expectations (Moment Generating Functions)
第5週	Chapter 1. Probability and Distribution Topic: Important Inequalities
第6週	Chapter 2. Multivariate Distributions Topics: Marginal Distributions and Moment Generating Functions of Bivariate Distributions
第7週	Chapter 2. Multivariate Distributions Topics: Conditional Distributions ‼️4/8 (Wednesday) is part of spring break and will be a day off from class.
第8週	Chapter 2. Multivariate Distributions Topics: Expectation and Variance of a Conditional Distribution
第9週	Chapter 2. Multivariate Distributions Topics: Independent Random Variables; Correlation Coefficient ‼️4/23 (Thursday) 18:30-21:00 Midterm Exam (I will run our classes as usual this week; please be present in classes.)
第10週	Chapter 2. Multivariate Distributions Topics: Extension to Several Random Variables; Transformations of Variables
第11週	Chapter 2. Multivariate Distributions Topics: Transformations of Variables; Jacobian of the Transformation
第12週	Chapter 2. Multivariate Distributions Chapter 3. Some Special Distributions Topic: Binomial and Related Distributions
第13週	Chapter 3. Some Special Distributions Topics: Poisson and Related Distributions
第14週	Chapter 3. Some Special Distributions Topics: Gamma and Chi-square Distributions
第15週	Chapter 3. Some Special Distributions Topics: Some Continuous Distributions ‼️6/4 (Thursday) 18:30-21:00 Terminal Exam.
第16週	I will schedule one class for you to review your marked exam sheets.
自主學習內容	01.參與專業論壇、講座、企業分享等產官學研相關交流活動 02.閱覽產業及學術相關多媒體資料

學習評量方式

✅ Midterm exam 4/23 (9th week) during 18:30~21:00: 35%
✅ Terminal exam 6/4 (15th week) during 18:30~21:00: 35%
✅ Miscellanea (including quizzes, class presence, etc.): 30%

教科書＆參考書目(書名、作者、書局、代理商、說明)

📚 Textbook:
Introduction to Mathematical Statistics, 8th Edition, by Robert V. Hogg, Joseph W. Mckean and Allen T. Craig.

📚 References:
TBA

課程教材（教師個人網址請列在本校內之網址）

🦉 iLearning

課程輔導時間

⏰ TBA

聯合國全球永續發展目標(連結網址)

提供體驗課程：N

請尊重智慧財產權及性別平等意識，不得非法影印他人著作。
更新日期西元年/月/日：2026/02/09 14:32:28	列印日期西元年/月/日：2026 / 3 / 22
MyTB教科書訂購平台：http://www.mytb.com.tw/