Course title 
Probability and Statistics 
Semester 
1042 
Designated for 
DEPARTMENT OF ELECTRICAL ENGINEERING 
Instructor 
SHI CHUNG CHANG 
Curriculum Number 
EE2007 
Curriculum Identity Number 
901 21000 
Class 
04 
Credits 
3 
Full/Half Yr. 
Half 
Required/ Elective 
Required 
Time 
Monday 4(11:20~12:10) Thursday 8,9(15:30~17:20) 
Remarks 
The upper limit of the number of students: 50. 
Ceiba Web Server 
http://ceiba.ntu.edu.tw/1042_Prob_E 
Course introduction video 

Table of Core Capabilities and Curriculum Planning 
Table of Core Capabilities and Curriculum Planning 
Course Syllabus

Please respect the intellectual property rights of others and do not copy any of the course information without permission

Course Description 
Tentative Course Outline:
1. Experiments, Models, and Probabilities
1.1. Applying Set Theory to Probability
1.2. Probability Axioms
1.3. Some Consequences of the Axioms
1.4. Conditional Probability
1.5. Independence
1.6. Sequential Experiments and Tree Diagrams
2. Random Variables
2.1. Definitions
2.2. Probability Mass Function
2.3. Families of Discrete Random Variables
2.4. Cumulative Distribution Function (CDF)
2.5. Probability Density Function
2.6. Families of Continuous Random Variables
3. Random Variables and Expected Value
3.1. Conditional Probability Mass/Density Function
3.2. Probability Models of Derived Random Variables
3.3. Average
3.4. Variance and Standard Deviation
3.5. Expected Value of a Derived Random Variable
Midterm exam
4. Random Vectors
4.1. Probability Models of N Random Variables
4.2. Vector Notation
4.3. Joint Cumulative Distribution Function
4.4. Joint Probability Mass/Density Function
4.5. Marginal PMF/PDF
4.6. Functions of Two Random Variables (Jacobian Transformation)
4.7. Conditioning by a Random Variables
4.8. Bivariate Gaussian Random Variables
4.9. Correlation Matrix
5. Sums of Random Variables
5.1. Expected Values of Sums
5.2. PDF of the Sum of Two Random Variables
5.3. Moment Generating Functions
5.4. MGF of the Sum of Independent Random Variables
5.5. Random Sums of Independent Random Variables
5.6. Central Limit Theorem
5.7. Applications of the Central Limit Theorem
5.8. The Chernoff Bound
6. Parameter Estimation Using the Sample Mean
6.1. Sample Mean: Expected Value and Variance
6.2. Deviation of a Random Variable from the Expected Value
6.3. Point Estimates of Model Parameters
6.4. Confidence Intervals
7. Hypothesis Testing
7.1. Significance Testing
7.2. Binary Hypothesis Testing
Final exam 
Course Objective 
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. 
Course Requirement 
Calculus (A) 1 & 2 
Office Hours 
每週一 12:10~13:10 每週四 12:30~13:30 Note: TBD 
References 
Will be provided in class. 
Designated reading 
Probability and Stochastic Processes (2nd Edition) by R.D. Yates, D.J. Goodman, John Wiley and Sons, 2005 
Grading 
No. 
Item 
% 
Explanations for the conditions 
1. 
Participation 
5% 

2. 
Homework and recitation problems 
25% 

3. 
Final exam 
35% 

4. 
Midterm exam 
35% 


Week 
Date 
Topic 
Week 1 
02/22, 25 
1.1 Motivation and Course overview
1.2 Applying Set Theory to Probability
1.3 Probability Axioms 
Week 2 
03/03 
1.3 Probability Axioms (Cont.)
1.4 Some Consequences of the Axioms
1.5 Conditional Probability; 
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 
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 3.13.4, 4.14.2
Recitation 2: BL 113, 18:0019:00, 3/16/2016 
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! 
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, 18:0019:00, 3/30/2016 
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, 18:0019:00, 4/6/2016 
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, 18:0019:00, 4/13/2016 
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, 18:0019:00, 4/20/2016 
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 
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, 18:0019:00, 4/27/2016 
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
Covariance, Correlation and Independence
Bivariate Gaussian R. Vs.
Reading Assignment: Sections 5.6 ~ 5.9 
Week 12 
05/16, 05/19 
Pairs of Random Variables
Covariance, 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 
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 
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 
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 
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 
