Semester Offering: August
 

To provide the fundamental knowledge of Probability Theory which is widely used in analysis of data and computer communications. The fundamental principles of probability Theory are thoroughly presented and then applied in data communication networking.

 

Introduction to Probability Theory. Random Variables. Conditional Probability and Conditional Expectation. The Exponential Distribution and Poisson Process

 

None

 

I  Introduction to Probability Theory

  1. Sample Space and Events
  2. Probabilities Defined on Events
  3. Conditional Probabilities
  4. Independent Events
  5. Bayes' Fomula


II  Random Variables

  1. Random Variables
  2. Discrete Random variables
  3. Continuous Random Variables
  4. Expectation of a random Variables
  5. Jointly Distributed Random variables
  6. Moment Generating Functions
  7. Stochastic Processes

III  Conditional Probability and Conditional Expectation

  1. The Discrete case
  2. The Continuous case

IV  The Exponential Distribution and Poisson Process

  1. The Exponential Distribution
  2. The Poisson Process
  3. Generalizations of the Poisson Process

 

N/A

 

Lecture Notes

 

  • Sheldon M. Ross: Introduction to Probability Models, Fifth Edition, Academic Press, Inc. 1993
  • Athanasios Papoulis: Probability, random Variables and Stochastic Processes, Second Edition, McGraw-Hill International Editions 1984

 

Since, this course is a 1-credit course, there is only the final examination. Therefore, the final grade will be computed from the final examination (100%). Opened-book is normally used for the examination.