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
901 21000
Class
04
Credits
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
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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

References
Will be provided in class.