Course Syllabus

Course Information：

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

Spring Semester
Year 2025 341225 Probability 1 3.0 3 ▲ Chen, Shiang-Jiun 4CSIE2 79 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2025	341225	Probability	1	3.0	3	▲	Chen, Shiang-Jiun	4CSIE2	79	0

Course Plan：

Instructor Chen, Shiang-Jiun　Office Hours

Email annette@ntut.edu.tw

Last Updated 2024-12-16 21:42:12

Course Objective 1.組合分析2.機率公設3.條件機率與獨立4.離散隨機變數5.連續隨機變數6.結合分佈隨機變數7.期望值性質8.極限定理9.模擬 1.Combinatorial Analysis 2.Axioms of Probability3. Conditional Probability and Independence4.Discrete Random Variables5.Continuous Random Variables6.Jointly Distributed Random Variables7.Properties of Expectation 8.Limit Theorems 9.Simulation

Course Schedule Week 1. Introduction to Probability; Counting Principle Week 2. Permutations and Combinations Week 3. Sample Spaces, Event and Axioms of Probability Week 4. Some Propositions; Equally Likely Fundamental Events Week 5. Conditional Probability; Bayes Formula Week 6. Independent Events; Sequential Events Week 7. Midterm 1; Random Variables Week 8. Discrete random Variable, CDF, PMF Week 9. Expectation, Variance, and Well Known Discrete Random Variables. Week 10. Continuous Random Variable and PDF Week 11. Well Known Continuous random Variables Week 12. Function of a Random Variable; Midterm 2 Week 13. Two and Multi Dimensional Random Variables Week 14. (Expectations of) Sums of Random Variables Week 15. Correlation and Covariance; Conditional Expectation Week 16. Inequality, the Law of Large Numbers and Limit Theorems Week 17. Selected Topics (Poisson Process, Markov Chain etc) Week 18. Final Exam

Evaluation and grading policy 1. Homeworks + Class participation 20% 2. Two Mid Terms 25%*2=50% 3. Final Exam. 30%

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
Textbook: Ghahramani, “Fundamentals of Probability with Stochastic Processes,” 3rd ed., Pearson, 2005 (or PNIE edition, 2014) , or 4th ed., CRC Press, 2019. Reference Books: 1. S. Ross, “A First Course in Probability”, 7th ed., Pearson Prentice Hall, 2006. 2. Leon-Garcia, “Probability and Random Processes for Electrical Engineering,” 3rd ed., Pearson, 2009. 3. Yates and Goodman, “Probability and Stochastic Processes,” 3rd ed., John Wiley & Sons, 2015. 4. Papoulis and Pillai, “Probability, Random Variables, and Stochastic Processes,” 4th ed., Mc-Graw-Hill, 2002. 5. Walpole, Myers, Myers and Ye, “Probability and Statistics for Engineers and Scientists,” 9th ed., Pearson, 2016.

The access to curricular consultation Office hours: Mon 10:10-12 14:00-18:00
https://irs.zuvio.com.tw/teacher/course/
email: annette@ntut.edu.tw

The course corresponds to the SDGs SDG4：優質教育（Quality Education）
SDG5：性別平等（Gender Equality）

Does the course incorporate AI

Note
　

Instructor	Chen, Shiang-Jiun　Office Hours
Email	annette@ntut.edu.tw
Last Updated	2024-12-16 21:42:12
Course Objective	1.組合分析2.機率公設3.條件機率與獨立4.離散隨機變數5.連續隨機變數6.結合分佈隨機變數7.期望值性質8.極限定理9.模擬 1.Combinatorial Analysis 2.Axioms of Probability3. Conditional Probability and Independence4.Discrete Random Variables5.Continuous Random Variables6.Jointly Distributed Random Variables7.Properties of Expectation 8.Limit Theorems 9.Simulation
Course Schedule	Week 1. Introduction to Probability; Counting Principle Week 2. Permutations and Combinations Week 3. Sample Spaces, Event and Axioms of Probability Week 4. Some Propositions; Equally Likely Fundamental Events Week 5. Conditional Probability; Bayes Formula Week 6. Independent Events; Sequential Events Week 7. Midterm 1; Random Variables Week 8. Discrete random Variable, CDF, PMF Week 9. Expectation, Variance, and Well Known Discrete Random Variables. Week 10. Continuous Random Variable and PDF Week 11. Well Known Continuous random Variables Week 12. Function of a Random Variable; Midterm 2 Week 13. Two and Multi Dimensional Random Variables Week 14. (Expectations of) Sums of Random Variables Week 15. Correlation and Covariance; Conditional Expectation Week 16. Inequality, the Law of Large Numbers and Limit Theorems Week 17. Selected Topics (Poisson Process, Markov Chain etc) Week 18. Final Exam
Evaluation and grading policy	1. Homeworks + Class participation 20% 2. Two Mid Terms 25%*2=50% 3. Final Exam. 30%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook: Ghahramani, “Fundamentals of Probability with Stochastic Processes,” 3rd ed., Pearson, 2005 (or PNIE edition, 2014) , or 4th ed., CRC Press, 2019. Reference Books: 1. S. Ross, “A First Course in Probability”, 7th ed., Pearson Prentice Hall, 2006. 2. Leon-Garcia, “Probability and Random Processes for Electrical Engineering,” 3rd ed., Pearson, 2009. 3. Yates and Goodman, “Probability and Stochastic Processes,” 3rd ed., John Wiley & Sons, 2015. 4. Papoulis and Pillai, “Probability, Random Variables, and Stochastic Processes,” 4th ed., Mc-Graw-Hill, 2002. 5. Walpole, Myers, Myers and Ye, “Probability and Statistics for Engineers and Scientists,” 9th ed., Pearson, 2016.
The access to curricular consultation	Office hours: Mon 10:10-12 14:00-18:00 https://irs.zuvio.com.tw/teacher/course/ email: annette@ntut.edu.tw
The course corresponds to the SDGs	SDG4：優質教育（Quality Education） SDG5：性別平等（Gender Equality）
Does the course incorporate AI
Note