機率
Probability
| 節 | 週二 | 週五 |
|---|---|---|
2 09:00–09:50 | 機率 ED203（光復） | |
5 13:20–14:10 | 機率 ED203（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
The goal of this course is to teach the fundamental theories, results, and applications of probability. Major topics in this course include but are not limited to discrete and continuous random variables, expectation and moments, functions of multiple random variables, covariance and correlation, conditional probability and expectation, Transforms of random variables, limit theorems, and a brief introduction to discrete time Markov chains. Applications and examples of probability theory will include but are not limited to wireless systems and networks and machine learning.
Calculus. Some understanding of linear algebra is recommended.
無備註
Course materials will be provided on New e3 system.
Homework (will include 8~12 problem sets): 30% Midterm Exam: 30% Final Exam: 35% In-class participation and in-class performance: 5%
Sample Space and Probability
Chapter 1
- 講授：
- 6
Discrete Random Variables
Chapter 2
- 講授：
- 9
Continuous and General Random Variables
Chapter 3
- 講授：
- 12
Further Topics on Random Variables
Chapter 4
- 講授：
- 9
Limit Theorems
Chapter 5
- 講授：
- 9
An Introduction to Discrete-Time Markov Chains
7.1 Discrete-Time Markov Chains 7.2 Classification of States 7.3 Steady-state behavior
- 講授：
- 6
Selected topics
Poisson processes, Bayesian statistical inference, fundamental of queuing theory, etc.
- 講授：
- 3
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 1: sample space and probability, conditional probability and independence 2025-02-18(二),2025-02-21(五) |
| 第 2 週 | Chapter 2: discrete random variables, probability mass function 2025-02-25(二),2025-02-28(五) |
| 第 3 週 | Chapter 2: functions of random variables, expectation and variance 2025-03-04(二),2025-03-07(五) |
| 第 4 週 | Chapter 2: joint PMF, conditioning independence 2025-03-11(二),2025-03-14(五) |
| 第 5 週 | Chapter 3: continuous random variables, cumulative distribution functions 2025-03-18(二),2025-03-21(五) |
| 第 6 週 | Chapter 3: Normal random variables 2025-03-25(二),2025-03-28(五) |
| 第 7 週 | Chapter 3: joint PDFs of multiple random variables 2025-04-01(二),2025-04-04(五) |
| 第 8 週 | Chapter 3: conditioning for continuous random variables, The continuous Bayes' rules 2025-04-08(二),2025-04-11(五) |
| 第 9 週 | Midterm exam 2025-04-15(二),2025-04-18(五) |
| 第 10 週 | Chapter 4: Derived distributions, covariance and correlation, conditional expectation and variance as random variables 2025-04-22(二),2025-04-25(五) |
| 第 11 週 | Chapter 4: Transforms, sum of a random number of independent random variables 2025-04-29(二),2025-05-02(五) |
| 第 12 週 | Chapter 5: Markov and Chebyshev inequalities, The weak law of large numbers 2025-05-06(二),2025-05-09(五) |
| 第 13 週 | Chapter 5: Convergence in probability, central limit theorem 2025-05-13(二),2025-05-16(五) |
| 第 14 週 | Chapter 5: The strong law of large numbers 2025-05-20(二),2025-05-23(五) |
| 第 15 週 | Chapter 7: Concept of stochastic processes, discrete-time Markov chains 2025-05-27(二),2025-05-30(五) |
| 第 16 週 | Chapter 7: Steady-state behavior of Markov chains Selected topics: Poisson process, Bayesian statistical inference, fundamental of queuing theory, etc. 2025-06-03(二),2025-06-06(五) |
| 第 17 週 | Final exam preparation week. 2025-06-10(二),2025-06-13(五) |
| 第 18 週 | Final exam 2025-06-17(二),2025-06-20(五) |
Introduction to Probability, 2nd Edition, D. P. Bertsekas and J. N. Ysitsiklis, Athena Scientific, 2008.
- 地點
- ED 833.
- 時間
- Friday 10:00~12:00
- 聯絡方式
- Email: mingchunlee@nycu.edu.tw 助教:TBD (at ED 821)