NCHU Course Outline

Course Name	(中) 機率論(2260)
	(Eng.) Introduction to Probability
Offering Dept	Department of Applied Mathematics
Course Type	Required	Credits	3	Teacher	沈宗荏
Department	Department of Applied Mathematics/Undergraduate	Language	English	Semester	2026-SPRING
Course Description	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).
Prerequisites				self-directed learning in the course	Y

Relevance of Course Objectives and Core Learning Outcomes(%)			Teaching and Assessment Methods for Course Objectives
Course Objectives	Competency Indicators	Ratio(%)	Teaching Methods	Assessment Methods
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.Professional Knowledge in Statistical Analysis 6.Theory of Mathematical Analysis, Statistics, and Mechanics	70 30	Lecturing Discussion Other	Other Quiz Assignment Attendance Written Presentation
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Chapter 1. Probability and Distribution Topics: Review of Set Notations; Probability Set Functions Week 2 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. Week 3 Chapter 1. Probability and Distribution Topics: Random Variables; Cumulative Distribution Functions Week 4 Chapter 1. Probability and Distribution Topics: Expectation of a Random Variable; Some Special Expectations (Moment Generating Functions) Week 5 Chapter 1. Probability and Distribution Topic: Important Inequalities Week 6 Chapter 2. Multivariate Distributions Topics: Marginal Distributions and Moment Generating Functions of Bivariate Distributions Week 7 Chapter 2. Multivariate Distributions Topics: Conditional Distributions ‼️4/8 (Wednesday) is part of spring break and will be a day off from class. Week 8 Chapter 2. Multivariate Distributions Topics: Expectation and Variance of a Conditional Distribution Week 9 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.) Week 10 Chapter 2. Multivariate Distributions Topics: Extension to Several Random Variables; Transformations of Variables Week 11 Chapter 2. Multivariate Distributions Topics: Transformations of Variables; Jacobian of the Transformation Week 12 Chapter 2. Multivariate Distributions Chapter 3. Some Special Distributions Topic: Binomial and Related Distributions Week 13 Chapter 3. Some Special Distributions Topics: Poisson and Related Distributions Week 14 Chapter 3. Some Special Distributions Topics: Gamma and Chi-square Distributions Week 15 Chapter 3. Some Special Distributions Topics: Some Continuous Distributions ‼️6/4 (Thursday) 18:30-21:00 Terminal Exam. Week 16 I will schedule one class for you to review your marked exam sheets. self-directed learning    01.Participation in professional forums, lectures, and corporate sharing sessions related to industry-government-academia-research exchange activities.    02.Viewing multimedia materials related to industry and academia.
Evaluation
✅ 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%
Textbook & other References
📚 Textbook: Introduction to Mathematical Statistics, 8th Edition, by Robert V. Hogg, Joseph W. Mckean and Allen T. Craig. 📚 References: TBA
Teaching Aids & Teacher's Website
🦉 iLearning
Office Hours
⏰ TBA
Sustainable Development Goals, SDGs(Link URL)
include experience courses：N

Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2026/02/09 14:32:28	Printed Date, year/month/day：2026 / 3 / 10
The second-hand book website：http://www.myub.com.tw/