機率
Probability
| 節 | 週二 | 週五 |
|---|---|---|
2 09:00–09:50 | 機率 ED203 | |
5 13:20–14:10 | 機率 ED203 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.
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
- Discrete Random Variables
- Continuous and General Random Variables
- Further Topics on Random Variables
- Limit Theorems
- An Introduction to Discrete-Time Markov Chains
- Selected topics
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 1: sample space and probability, conditional probability and independence |
| 第 2 週 | Chapter 2: discrete random variables, probability mass function |
| 第 3 週 | Chapter 2: functions of random variables, expectation and variance |
| 第 4 週 | Chapter 2: joint PMF, conditioning independence |
| 第 5 週 | Chapter 3: continuous random variables, cumulative distribution functions |
| 第 6 週 | Chapter 3: Normal random variables |
| 第 7 週 | Chapter 3: joint PDFs of multiple random variables |
| 第 8 週 | Chapter 3: conditioning for continuous random variables, The continuous Bayes' rules |
| 第 9 週 | Midterm exam |
| 第 10 週 | Chapter 4: Derived distributions, covariance and correlation, conditional expectation and variance as random variables |
| 第 11 週 | Chapter 4: Transforms, sum of a random number of independent random variables |
| 第 12 週 | Chapter 5: Markov and Chebyshev inequalities, The weak law of large numbers |
| 第 13 週 | Chapter 5: Convergence in probability, central limit theorem |
| 第 14 週 | Chapter 5: The strong law of large numbers |
| 第 15 週 | Chapter 7: Concept of stochastic processes, discrete-time Markov chains |
| 第 16 週 | Chapter 7: Steady-state behavior of Markov chains Selected topics: Poisson process, Bayesian statistical inference, fundamental of queuing theory, etc. |
| 第 17 週 | Final exam preparation week. |
| 第 18 週 | Final exam |
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)