課程資訊
課程名稱
 機率與統計
Probability and Statistics 
開課學期
 102-2 
授課對象
 電機工程學系  
授課教師
 張時中 
課號
 EE2007 
課程識別碼
 901E21000 
班次
 05 
學分
 3 
全/半年
 半年 
必/選修
 必修 
上課時間
 星期一4(11:20~12:10)星期四7,8(14:20~16:20) 
上課地點
 電二102電二102 
備註
 本系學生優先修習
總人數上限：50人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1022prob_stats_SCC 
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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
 

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.
 
課程要求
 Grading: Homework : 20%, Midterm : 40%, Final : 40%, Participation 5% 
預期每週課後學習時數
  
Office Hours
 每週一 12:10~13:10
每週四 12:30~13:30 備註： TBD 
指定閱讀
  
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.  
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
Week 1
 02/17, 02/21  1.1 Motivation and Course overview
1.2 Applying Set Theory to Probability
1.3 Probability Axioms

 
Week 2
 03/03, 03/06  1.3 Probability Axioms (Cont.)
1.4 Some Consequences of the Axioms
1.5 Conditional Probability;
1.6 Independence
 
Week 3
 03/03, 03/06  Independence
Sequential Experiments and Tree Diagrams
Discrete Random Variables: Definitions
Probability Mass Function
 
Week 4
 3/10, 3/13  Discrete Random Variables:Definition;
Probability Mass Function;
Families of Discrete Random Variables;
Reading Assignment: Sections 2.2-2.4
 
Week 5
 3/17, 3/20  Families of Discrete Random Variables (Cont.):
Uniform;
Poisson.
Cumulative Distribution Function (CDF):
DRV;
CRV (3.1);
Probability Density Function (3.2);
Families of CRVs (3.4)
Reading Assignment: Sections 2.4, 3.1, 3.2, 3.3.
 
Week 6
 3/24, 3/27  Averages and Expected Values of R. V. (2.5, 2.6, 3.3 , Cont.);
Families of Continuous Random Variables (3.4);
Gaussian Random Variables (3.5);
Reading Assignment: Sections 2.5-2.6, 3.3-3.5.
 
Week 7
 3/31, 4/3  Gaussian Random Variables (3.5, Cont.);
Probability Models of Derived Random Variables (2.6, 3.7);
Conditional Probability Mass/Density Function (2.9, 3.8).
Reading Assignment: Sections 2.6, 2.9, 3.5, 3.7, 3.8
 
Week 8
 04/07, 04/10  Averages and Expected Values of R. V. (2.5, 2.6, 3.3, Cont.)
Gaussian Random Variables (3.5)
Probability Models of Derived Random Variables (2.6, 3.7)
Conditional Probability Mass/Density Function (2.9, 3.8)
Conditional Expectation
Reading Assignment: Sections 2.6, 2.9, 3.5, 3.7, 3.8
 
Week 9
 04/21, 04/24  Random Vector:
Probability Models of N Random Variables;
Vector Notation.
Pairs of R.Vs.:
Joint CDF;
Joint PMF;
Marginal PMF.
Reading Assignment: Sections 5.1, 5.2, 4.1-4.3
 
Week 10
 04/28, 05/01  Pairs of R.Vs.:
Marginal PMF (Cont.);
Joint PDF;
Marginal PDF;
Functions of Two R.Vs;
Reading Assignment: Sections 4.3-4.6.
 
Week 11
 05/05, 05/08  Pairs of R.Vs.:
Two Functions of Two R.Vs
Expected Values;
Conditioning by an Event;
Conditional PDF;
Independence between Two R.Vs;
Reading assignments: Secs. 4.7-4.10, Transformation of 2 RVs 
Week 12
 05/12, 05/15  Pairs of R.Vs.:
Independence between Two R.Vs (Cont.);
Bivariate R.V.s;
Introduction to Filtering and Estimation;
Reading Assignment:
Sections 4.10-4.11, 5.4*-5.7*;
Kalman filter: simple example.
 
Week 13
 5/19, 5/22  Sums of R. V.s:
PDF of the Sum of Two R.V.s (Cont.);
Moment Generating Functions;
Histogram, Skewness, Kurtosiss, and Construction of pdf from Data;
MGF of the Sum of Indep. R.Vs;
Random Sums of Indepent R.Vs.
Reading Assignment:
Textbook Sections 6.1-6.5, Supplementary Materials
 
Week 14
 5/26, 5/29  Random Sums of Indepent R.Vs (Cont.);
Central Limit Theorem;
Application of the Central Limit Theorem;
The Chernoff Bound.
Parameter Estimation Using the Sample Mean
Sample Mean: Expected Value and Variance
Reading Assignment: 6.7 – 6.8, 7.1
 
Week 15
 06/05  Parameter Estimation Using the Sample Mean
Sample Mean: Expected Value and Variance (Cont.)
Deviation of a Random Variable from the Expected Value
Point Estimates of Model Parameters
Confidence Intervals
Reading Assignment: 7.1-7.4 
Week 16
 06/09  Parameter Estimation Using the Sample Mean:
Point Estimates of Model Parameters (Cont.);
Confidence Intervals.
Reading Assignment: 7.3-7.4, Supplementary Materials
 
Week 17
 06/19  Final Exam
15:30 – 17:30 6/16
Coverage: Chapters 4, 6 and 7
(Chapter 5: two variables and iid)
 
Week 18
 06/23  Significance Testing
Binary Hypothesis Testing
Reading Assignment: 8.1 - 8.2