機率(英文班)
Probability
| 節 | 週二 | 週五 |
|---|---|---|
2 09:00–09:50 | 機率(英文班) ED103（光復） | |
5 13:20–14:10 | 機率(英文班) ED103（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
Teach the theory and applications of calculus-based probability theory. Applications of probability theory include but are not limited to wireless communication systems, computer networking, and machine learning.
calculus, linear algebra.
無備註
Lectures.
Homework and in-class performance: 20% Midterm Exam: 40% Final Exam: 40%
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: derived random variables, moment generating function, conditional expectation as a random variable.
- 講授：
- 12
Limit Theorems:
Chapter 5: Markov inequality, law of large numbers, central limit theorem.
- 講授：
- 9
An Introduction to Discrete-Time Markov Chains
7.1 Discrete-Time Markov Chains and examples 7.3 Steady-state behavior
- 講授：
- 6
-
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 1: sample space and probability, conditional probability and independence Chapter 2: discrete random variables, probability mass function |
| 第 2 週 | Chapter 2: functions of random variables, expectation and variance |
| 第 3 週 | Chapter 2: joint PMF, conditioning independence |
| 第 4 週 | Chapter 3: continuous random variables, cumulative distribution functions, probability density functions. |
| 第 5 週 | Chapter 3: Normal/Gaussian random variables. |
| 第 6 週 | Chapter 3: joint PDFs of multiple random variables, conditioning for continuous random variables. |
| 第 7 週 | Chapter 3: The continuous Bayes' rules |
| 第 8 週 | Midterm Exam |
| 第 9 週 | Chapter 4: Derived distributions, covariance and correlation |
| 第 10 週 | Chapter 4: Transforms |
| 第 11 週 | Chapter 4: conditional expectation and variance as random variables |
| 第 12 週 | Chapter 4: Sum of a random number of independent random variables |
| 第 13 週 | Chapter 5: Markov and Chebyshev inequalities, The weak law of large numbers |
| 第 14 週 | Chapter 5: Convergence in probability, central limit theorem. |
| 第 15 週 | Chapter 5: The strong law of large numbers. |
| 第 16 週 | Chapter 7: Discrete-time Markov chains |
| 第 16 週 | Final exam |
| 第 17 週 | Chapter 7: Steady-state behavior of Markov chains |
Introduction to Probability, 2nd Edition, D. P. Bertsekas and J. N. Ysitsiklis, Athena Scientific, 2008.
- 地點
- ED730
- 時間
- 5CD
- 聯絡方式
- Email: runghunggau@g2.nctu.edu.tw