Course Information
Course title
 Probability and Statistics 
Semester
 104-2 
Designated for
 DEPARTMENT OF ELECTRICAL ENGINEERING  
Instructor
 SHI CHUNG CHANG 
Curriculum Number
 EE2007 
Curriculum Identity Number
 901E21000 
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 
Student Workload (expected study time outside of class per week)
  
Office Hours
 Mon. 12:10~13:10
Thu. 12:30~13:30 Note: TBD 
Designated reading
 Probability and Stochastic Processes (2nd Edition) by R.D. Yates, D.J. Goodman, John Wiley and Sons, 2005 
References
 Will be provided in class. 
Grading
  
No.
Item
%
Explanations for the conditions
1. 
 Participation 
5% 
  
2. 
 Homework and recitation problems 
25% 
  
3. 
 Final exam 
35% 
  
4. 
 Midterm exam 
35% 
  
 
Progress
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 3.1-3.4, 4.1-4.2
Recitation 2: BL 113, 18:00-19:00, 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, 18:00-19:00, 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, 18:00-19:00, 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, 18:00-19:00, 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, 18:00-19:00, 4/20/2016
 
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
 
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 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
 
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
 
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