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課程名稱 |
機率與統計
Probability and Statistics |
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開課學期 |
104-2 |
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授課對象 |
電機工程學系 |
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授課教師 |
張時中 |
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課號 |
EE2007 |
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課程識別碼 |
901E21000 |
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班次 |
04 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期一4(11:20~12:10)星期四8,9(15:30~17:20) |
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上課地點 |
電二102電二102 |
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備註 |
本課程以英語授課。本系學生優先修習
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042_Prob_E |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Experiments, Models, and Probabilities
2. Discrete Random Variables
3. Continuous Random Variables
4. Pairs of Random Variables
5. Random Vectors
6. Sums of Random Variables
7. Parameter Estimation Using the Sample Mean
8. Hypothesis Testing
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課程目標 |
To introduce to students the theory, models and analysis of probability and basic statistics and their applications with emphasis on electrical and computer engineering problems.
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課程要求 |
Grading: Homework : 20%, Midterm : 40%, Final : 40%, Participation 5% |
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預期每週課後學習時數 |
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Office Hours |
每週一 12:10~13:10
每週四 12:30~13:30 備註： TBD |
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指定閱讀 |
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參考書目 |
教科書： "Probability and Stochastic Processes - A Friendly
Introduction for Electrical and Computer Engineers," Second Edition
Authors : Roy D. Yates and David Goodman
Publisher : John Wiley & Sons, Inc., 2005. |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
02/22, 25 |
1.1 Motivation and Course overview
1.2 Applying Set Theory to Probability
1.3 Probability Axioms
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Week 2 |
03/03 |
1.3 Probability Axioms (Cont.)
1.4 Some Consequences of the Axioms
1.5 Conditional Probability;
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Week 3 |
03/07, 03/10 |
1.6 Independence
Chapter 2 Sequential Experiments and Tree Diagrams
3.1 Discrete Random Variables:
3.2 Definitions of Probability Mass Function
Reading Assignment: Chapter 2 and Sections 3.1, 3.2
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Week 4 |
03/13, 03/17 |
Definition of Random Variables
DRVs (Textbook 3.1)
CRVs (Textbook 4.1)
Probability Mass Function (Textbook 3.2)
Families of Discrete Random Variables (Textbook 3.3)
Reading Assignment: Sections 3.1-3.4, 4.1-4.2
Recitation 2: BL 113, 18:00-19:00, 3/16/2016
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Week 5 |
03/21, 03/24 |
Probability Mass Function of DRVs (Cont.)
Cumulative Distribution Functions (CDF)
DRVs (Textbook 3.4)
Definition and CDF of CRVs (Textbook 4.1)
Probability Density Function (4.3 in 3rd Edition)
Families of Continuous Random Variables (4.5 in 3rd Edition)
Reading Assignment: Sections 4.1~4.3,4.5
No Recitation this week!
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Week 6 |
03/28, 03/31 |
Uniform Random Variables  (Cont.) and Generation (4.4)
Averages and Expected Values of R. Vs. (3.5, 4.4)
Variance and Standard Deviation (3.8)
Families of Continuous Random Variables (4.5)
Functions of a Random Variable (3.6)
Reading Assignment: Sections 3.5, 3.6, 4.4, 4.5
Recitation 3: BL 113, 18:00-19:00, 3/30/2016
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Week 7 |
04/07 |
Families of Continuous Random Variables (Cont., 4.5)
Gaussian Random Variables (4.6)
Functions of a Random Variable (3.6)
Probability Models of Derived R.V. (6.2)
Reading Assignment: Sections 3.6, 4.5~4.6, 6.2
Recitation 4: BL 113, 18:00-19:00, 4/6/2016
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Week 8 |
4/11, 4/14 |
Gaussian Random Variables (Cont., 4.5~4.6)
Functions of a Random Variable (3.6)
Probability Models of Derived R.V. (6.2)
Reading Assignment: Sections 3.6, 4.5~4.6, 6.2
Recitation 5: BL 113, 18:00-19:00, 4/13/2016
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Week 9 |
4/18, 4/21 |
Probability Models of Derived R.V. (Cont.)
DRV (3.6)
CRV (6.2)
MRV (4.7, 6.3)
Random Variable Conditioned on an Event (7.1)
Conditional Expected Value Given an Event (7.2)
Reading Assignment: Sections 3.6, 6.2~6.3, 7.1~7.2
Previous midterm test sets
Recitation 6: BL 113, 18:00-19:00, 4/20/2016
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Week 10 |
4/25, 4/28 |
Joint CDF (5.1)
Midterm Exam (4/28) !!!
Reading Assignment:
Chapters 1~4 (excluding Sec. 4.7)
Sections: 6.2~6.3, 7.1~7.2
Recitation 7: BL 113, 18:00-19:00, 4/27/2016
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Week 10 |
05/02, 05/05 |
Multiple Random Variables
Joint CDF
Joint PMF
Marginal PMF
Joint pdf
Marginal pdf
Independent R.Vs.
Reading Assignment: Sections 5.1~ 5.6
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Week 11 |
05/09, 05/12 |
Pairs of Random Variables
Joint pdf (Cont.)
Marginal pdf
Independent R.Vs.
Expected Values of a Function of Two R.Vs
Co-variance, Correlation and Independence
Bivariate Gaussian R. Vs.
Reading Assignment: Sections 5.6 ~ 5.9
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Week 12 |
05/16, 05/19 |
Pairs of Random Variables
Co-variance, Correlation
Bivariate Gaussian R. Vs.
PMF of a Function of Two Discrete Random Variables (Sec. 6.1)
Continuous Functions of Two Continuous Random Variables (Sec. 6.4)
PDF of the Sum of Two Random Variables (Sec. 6.5)
Reading Assignment: Sections 5.8 ~ 5.9, 6.1, 6.4~6.5
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Week 13 |
05/23, 05/26 |
Pairs of Random Variables
Continuous Functions of Two Continuous Random Variables (Sec. 6.4, Cont.)
PDF of the Sum of Two Random Variables (Sec. 6.5)
Conditioning Two Random Variables by an Event (Sec. 7.3)
Conditioning by a Random Variable (Sec. 7.4)
Conditional Expected Value (Sec. 7.5)
Conditional PDF of Bivariate Gaussian
Reading Assignment: Sections 6.4~6.5, 7.3~7.6
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Week 14 |
05/30, 06/02 |
Sum of Random Variables
Conditional PDF of Bivariate Gaussian (Cont.)
Expected Values of Sum
Moment Generating Functions
MGF of the Sum of Indep. R.Vs.
Reading Assignment: Sections 7.6, 9.1 ~ 9.3
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Week 15 |
0606, 0612 |
This Week
Sum of Random Variables (Cont.)
- MGF of Random Sum of Indep. R.Vs.
- Central Limit Theorem and Applications
Deviation of a Random Variable from the Expected Value
Reading Assignment: Sections 9.4, 10.2 & Supplements
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Week 16 |
0613, 0616 |
Binary Hypothesis Testing
- Tests, Likelihood and Types of Errors
- MAP Test
- Minimum Cost Test
- Maximum Likelihood Test
Reading Assignment: Section 11.1
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