| Relevance of Course Objectives and Core Learning Outcomes(%) |
Teaching and Assessment Methods for Course Objectives |
| Course Objectives |
Competency Indicators |
Ratio(%) |
Teaching Methods |
Assessment Methods |
| This course develops a solid foundation in probability theory, including combinatorial methods, probability measures, and discrete and continuous random variables. Students will learn conditional probability, expectations, inequalities, and the analysis and transformation of random variables. Emphasis is placed on important probability distributions and their relationships. The course prepares students for further study in Mathematical Statistics I and II. |
| 3.Professional Knowledge in Statistical Analysis |
| 6.Theory of Mathematical Analysis, Statistics, and Mechanics |
|
|
| Exercises |
| Discussion |
| Lecturing |
|
|
| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
Combinatorial Analysis |
| Week 2 |
Set Theory and the probability set function |
| Week 3 |
Conditional probability, independence, and random variables |
| Week 4 |
Discrete random variables |
| Week 5 |
Continuous random variables |
| Week 6 |
Expectations |
| Week 7 |
Important inequalities |
| Week 8 |
Distributions and transformations of two random variables |
| Week 9 |
Midterm exam |
| Week 10 |
Conditional distributions and expectations |
| Week 11 |
Transformations for several random variables and extensions |
| Week 12 |
Linear combinations of random variables |
| Week 13 |
Binomial and Poisson distributions |
| Week 14 |
The gamma, beta, chi-square, and normal distributions |
| Week 15 |
Multivariate normal distributions, t- and F- distributions |
| Week 16 |
Final exam |
self-directed
learning |
02.Viewing multimedia materials related to industry and academia.
|
|
| Evaluation |
| Quizzes: 30%, Midterm Exam:35%, Final Exam: 35% |
| Textbook & other References |
Hogg, R. V., McKean, J. W., & Craig, A. T. (2019). Introduction to mathematical statistics. 8th Edition, Pearson Education. (華泰文化代理)
Ross, S. M. (2020). A first course in probability. 10th Edition, Pearson Education. (華泰文化代理) |
| Teaching Aids & Teacher's Website |
| The iLearning site will host the uploaded materials |
| Office Hours |
| Tuesday 13:00~15:00 |
| Sustainable Development Goals, SDGs(Link URL) |
| 08.Decent Work and Economic Growth 09.Industry, Innovation and Infrastructure | include experience courses：N |
|