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課程名稱 |
機率與統計
Probability and Statistics |
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開課學期 |
105-2 |
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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 |
3.0 |
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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/1052EE_PnS_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 |
每週四 12:30~13:30
每週一 12:10~13:10 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 |
02/20, 02/23 |
Announcement web site for 4 classes:
https://sites.google.com/site/ntueepas2017/
1.1 Motivation and Course overview
1.2 Applying Set Theory to Probability
1.3 Probability Axioms
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Week 2 |
02/27, 03/02 |
02/27 No Class
Probability Axioms
Some Consequences of the Axioms
Reading Assignment: Sections 1.1-1.3
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Week 3 |
03/06, 03/09 |
PSome Consequences of the Axioms (Cont.)
Conditional Probability
Independence
Sequential Experiments and Tree Diagrams
Discrete Random Variables: Definitions
Reading Assignment: Sections 1.3-1.6 3.1
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Week 4 |
03/13, 03/16 |
Definition of Random Variables
DRVs (Textbook 3.1)
Probability Mass Function (Textbook 3.2)
Families of Discrete Random Variables (Textbook 3.3)
Reading Assignment: Sections 3.1-3.4
Recitation
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Week 5 |
03/20, 03/23 |
Last Time (3/20)
12:20 – 13:10 1st makeup hour for 3/30
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)
Uniform Random Variables  (4.5 in 3rd Edition)
Reading Assignment: Sections 4.1~4.3,4.5
No Recitation!
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Week 5 |
3/27 |
17:30 – 18:20 2nd makeup hour for 3/30
Definition and CDF of CRVs (Cont., Textbook 4.1)
Probability Density Function (4.3 in 3rd Edition)
Uniform Random Variables (4.5 in 3rd Edition) and   Generation
Averages and Expected Values of R. Vs. (3.5, 4.4)
Variance and Standard Deviation (3.8)
Families of Continuous Random Variables (4.5)
Reading Assignment: Sections 3.5, 3.8, 4.1- 4.5
Recitation 3: BL 113, 18:30-19:30, 3/29/2017
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Week 6 |
4/6 |
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, 18:30-19:30, 4/13/2017
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Week 7 |
04/10, 4/13 |
(4/10 11:20 – 12:30, 4/13 15:30 – 18:00)
Gaussian Random Variables (4.6)
Functions of a Random Variable (3.6)
Probability Models of Derived R.V. (6.2)
Random Variable Conditioned on an Event (7.1) 
Conditional Expected Value Given an Event (7.2)
Joint Cumulative Distribution Function (5.1) 
Reading Assignment: Sections 3.6, 4.6, 6.2, 5.1
Recitation 4: BL 113, 18:30-19:30, 4/12/2017
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Week 8 |
4/17, 4/20 |
I. Joint PMF and PDF (Cont.)
II. Midterm exam and scope
1. Chapters 1~4
2. Secs 6.2 and 6.3
3. Secs. 7.1 and 7.2.
4. Secs 5.1, 5.2, 5.4 (Joint CDF, PMF and PDF)
Excluding Sec. 4.7 and Matlab Sections
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Week 9 |
4/24, 4/26 |
Brainteasers
Multiple Random Variables
Marginal PMF & PDF
Independent R.Vs.
Expected Values of a Function of Two R.Vs
Reading Assignment: Sections 5.3, 5.5~ 5.8
Recitation 5: BL 113, 18:30-19:30, 4/26/2017
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Week 10 |
5/1, 5/4 |
Multiple Random Variables
Co-variance, Correlation and Independence
Bivariate Gaussian R. Vs.
Continuous Functions of Two Continuous Random Variables
PDF of the Sum of Two Random Variables
Functions of Two Random Variables
Reading Assignment: Sections 5.8~ 5.10, 6.4, 6.5, 8.3
Recitation 6: BL 113, 18:30-19:30, 5/3/2017
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Week 11 |
5/8, 5/11 |
Multiple Random Variables
Continuous Functions of Two Continuous Random Variables
PDF of the Sum of Two Random Variables
Conditioning of Two Random Variables by an Event
Conditioning by a Random Variable
Conditional Expected Value Given a Random Variable
Bivariate Gaussian R. Vs: Conditional PDFs
Reading Assignment: Sections 6.4, 6.5, 7.1~7.6
Recitation 7: BL 113, 18:30-19:30, 5/10/2017
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Week 12 |
5/15, 5/18 |
Sum of Random Variables
Expected Values of Sum
Moment Generating Functions
MGF of the Sum of Indep. R.Vs.
Central Limit Theorem and Applications
Reading Assignment: Sections 9.1 ~ 9.4
Recitation 8: BL 113, 18:30-19:30, 5/17/2017
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Week 13 |
5/22, 5/25 |
Sum of Random Variables
MGF of the Sum of Indep. R.Vs.(Cont.)
Central Limit Theorem and Applications
Introductory Statistics
Sample Mean and Confidence Interval
Sample Mean: Expected Value and Variance
Deviation of a R.V.from the Expected Value
Markov, inequalitiy
Reading Assignment: Sections 9.4, 10.1, 10.2, Supplementary Reading
Recitation 8: BL 113, 18:30-19:30, 5/24/2017 |
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Week 14 |
05/29, 06/01 |
Introductory Statistics
Sample Mean and Confidence Interval
Deviation of a R.V.from the Expected Value
Chebychev inequality
Chernoff Bound
Confidence Interval
Reading Assignment: Sections 10.2,10.5, Chapter 11
Recitation 9: BL 113, 18:30-19:30, 6/7/2017
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Week 15 |
06/05, 06/08 |
Sample Mean
Relative Frequency Estimation of Probability
Sample Variance
Binary Hypothesis Testing
Tests, Likelihood and Types of Errors
MAP Test
Minimum Cost Test
Maximum Likelihood Test
Reading Assignment:
Sample Variance https://en.wikipedia.org/wiki/Bias_of_an_estimator#Sample_variance
Chapter 11
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Week 16 |
06/12, 06/15 |
06/12
Q&A of Past Final Exams by TA
06/15
Binary Hypothesis Testing (Cont.)
- Minimum Cost Test
- Maximum Likelihood Test
Reading Assignment: Section 11.1
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Week 17 |
06/22 |
Final Exam |
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