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課程名稱 |
機率與統計
Probability and Statistics |
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開課學期 |
107-2 |
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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 |
電二106電二106 |
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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/1072EE2007_04 |
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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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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 |
02/18, 02/21 |
Lecture 1 Experiments, Models, & Probabilities
1.1 Motivation and Course overview
1.2 Applying Set Theory to Probability
1.3 Probability Axioms
Reading Assignment: Sections 1.1-1.4
References:
1. P Diaconis, S Holmes, R Montgomery, “Dynamical bias in the coin toss,” SIAM review, 2007 , Vol. 49, No. 2, pp211-235.
2. Darrell Huff, How to Lie with Statistics, Penguin Books 1973
http://archive.org/details/HowToLieWithStatistics
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Week 2 |
02/25 |
Applying Set Theory to Probability
Probability Axioms
Reading Assignment: Sections 1.1-1.4
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Week 3 |
3/4,3/7 |
Probability Axioms (Cont.)
Conditional Probability
Independence
Sequential Experiments and Tree Diagrams
Reading Assignment: Sections 1.5-1.7 |
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Week 4 |
3/11, 3/14 |
PSequential Experiments and Tree Diagrams (Cont.)
Discrete Random Variables (DRVs): Definitions
DRVs: Probability Mass Functions
Families of Discrete Random Variables (Textbook 3.3)
Reading Assignment: Sections 3.1-3.3
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Week 5 |
3/18, 3/21 |
Families of DRVs (Cont.)
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
Reading Assignment: Sections 3.5, 3.8, 4.1- 4.3, 4.5
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Week 6 |
3/25, 3/28 |
Probability Density Function (4.3 in 3rd Edition)
Uniform Random Variables (4.5 in 3rd Edition) and Generation
Averages (3.5)
Expected Value of Continuous Random Variables (3.5, 4.4)
Reading Assignment: Sections 3.6, 3.7, 4.3-4.4 |
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Week 7 |
4/1, 4/4 |
Families of Continuous Random Variables (4.5)
Reading Assignment: Section 4.5
4/4 Spring Break (no class) |
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Week 8 |
4/8, 4/11 |
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)
Reading Assignment: Sections 3.6, 4.6, 6.2, 7.1
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Week 9 |
4/15, 4/18 |
Random Variable Conditioned on an Event (7.1, Cont.)
Joint Probability Distributuion Function (5.1)
II. 4/18 Midterm exam and scope
Chapters 1~3
1. Experiments, Models, and Probabilities (Ch 1 & 2 in 3rd Edition) 1.1. Applying Set Theory to Probability (1.1 in 3rd Edition) 1.2. Probability Axioms (1.2 in 3rd Edition) 1.3. Some Consequences of the Axioms (1.2 in 3rd Edition)
1.4. Conditional Probability (1.3 in 3rd Edition)
1.5. Independence (1.5 in 3rd Edition)
1.6. Sequential Experiments and Tree Diagrams (Ch 2 in 3rd Edition)
2. Random Variables (Ch 3 & 4 in 3rd Edition)
2.1. Definitions (3.1 in 3rd Edition)
2.2. Probability Mass Function (3.2 in 3rd Edition)
2.3. Families of Discrete Random Variables (3.3 in 3rd Edition)
2.4. Cumulative Distribution Function (CDF) (3.4 in 3rd Edition)
2.5. Probability Density Function (4.3 in 3rd Edition) 2.6. Families of Continuous Random Variables (4.5 in 3rd Edition)
3. Random Variables and Expected Value (Ch 3, 6 & 7 in 3rd Edition)
3.1. Conditional Probability Mass/Density Function (Ch 7 in 3rd Edition)
3.2. Probability Models of Derived Random Variables (Ch 6 in 3rd Edition)
3.3. Average (3.5 in 3rd Edition)
3.4. Variance and Standard Deviation (3.8 in 3rd Edition)
3.5. Expected Value of a Derived Random Variable (3.7 in 3rd Edition)
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Week 10 |
4/29, 5/2 |
Multiple Random Variables
Marginal PMF & PDF (Cont.)
Independent R.Vs.
Expected Values of a Function of Two R.Vs
Co-variance, Correlation and Independence
Bivariate Gaussian R. Vs.
Reading Assignment: Sections 5.5~ 5.9
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Week 10 |
4/22, 4/26 |
Brainteasers
Multiple Random Variables
Joint Cumulative Distribution Function
Joint PMF
Joint PDF
Marginal PMF & PDF
Independent R.Vs.
Reading Assignment: Sections 5.1~ 5.6
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Week 11 |
5/6, 5/9 |
Multiple Random Variables
Co-variance, Correlation and Independence
Bivariate Gaussian R. Vs.
Continuous Functions of Two CRVs
PDF of the Sum of Two R.Vs
Conditioning Two RVs on an Event
Reading Assignment: Sections 5.8~5.10, 6.4, 6.5
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Week 12 |
5/13, 5/16 |
Continuous Functions of Two CRVs
PDF of the Sum of Two R.Vs
Conditioning Two RVs on an Event
Conditioning by a RV
Conditional Expected Value Given a Random Variable
Reading Assignment: Sections 7.3~7.6, 9.1
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Week 13 |
5/20, 5/23 |
Multiple Random Variables
Conditional Expected Value Given a Random Variable (Cont.)
Bivariate Gaussian R. Vs: Conditional PDFs
Sum of Random Variables
Expected Values of Sum
Moment Generating Functions
MGF of the Sum of Indep. R.Vs.
Reading Assignment: Sections 7.5 ~ 7.6, 9.1 ~ 9.3 |
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Week 14 |
5/27, 5/30 |
Sum of Independent Random Variables
Random Sum of Independent Random Variables
Central Limit Theorem (CLT)
CLT Applications
Reading Assignment: Sections 9.4
Supplementary Reading
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Week 15 |
06/03, 06/06 |
Unit 15-1
CLT Applications
Reading Assignment: Section 9.4 &
Supplementary Reading
Unit 15-2
Introduction to Statistics
Sample Mean: Expected Value and Variance
Deviation of a R.V.from the Expected Value
Markov inequality
Chebychev inequality
Chernoff Bound
Confidence Interval
Reading Assignment: Sections 10.1, 10.2, 10.5 Supplementary Reading
Unit 15-3
Confidence Interval and Sample Variance
Video: https://www.space.ntu.edu.tw/navigate/s/EA09427E2F6A41CAA143FBCF738C0361QQY |
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Week 16 |
6/10, 6/13 |
Binary Hypothesis Testing
Tests, Likelihood and Types of Errors
MAP Test
Minimum Cost Test
Maximum Likelihood Test
Reading Assignment:
Chapter 11
06/12 Recitation:Q&A of Past Final Exams |
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Week 17 |
6/20 |
Final Exam |
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