T RYERSON UNIVERSITY
Department of Electrical and Computer Engineering
EE8103 – Random Processes - Winter 2009
Course Information 

Last Updated on: December 29, 2008

ANNOUNCEMENTSU

  • The first lecture will be held on January 15 at ENG LG 12. The lecture notes are posted on this page.

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UINSTRUCTOUURU

 

Dr. Yifeng He

  • Office: ENG 324
  • Tel.: 4904
  • Email: yhe@ee.ryerson.ca

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LECTURE HOURS, ROOM, CONSULTING HOURSU

  • Lectures: Every Thursday, 6 - 9 PM at ENG LG 12
  • Consulting Hours: Every Thursday, 3 - 5 PM at ENG 324

UCOURSE EVALUATIONU

  • Quizzes: 4 * 5% = 20%
  • Midterm Exam: 35%
  • Final Exam: 45%

NOTES:

  • Assignments: There are 5 assignments. Students are expected to solve all the assignment problems. Information about these assignments will be posted on the course homepage. Although the assignments will not be collected, it is highly suggested student do the assignment problems by themselves.
  • Quizzes: 4 in-class quizzes, each 30 minutes and 5% weight.
  • Midterm Exam and Final Exam: each is a 3-hour closed-book exam.

 

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TEXTBOOKU

  • R.D. Yates and D. J. Goodman, Probability and Stochastic Processes, a friendly introduction for electrical and computer engineering, Second Edition, John Wiley & Sons Inc., 2004.

 

OTHER REFERENCES:

  • Sheldon M. Ross, Introduction to Probability Models, Eighth Edition, Academic Press, 2003.
  • A. Papoulis and S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, McGraw Hill 2002.
  • M. H. DeGroot and M. J. Schervish, Probability and Statistics, Addison Wesley, third edition, 2002.
  • P. Z. Peebles JR, Probability Random Variables and Random Signal Principles, McGraw-Hill.

 

CONTENTSU

  • Chapter 1: Experiments, Models, and Probabilities
    • Set Operation
    • Sample Space, Events and Probabilities
    • Probability Axioms
    • Conditional Probability
    • Independence
    • Bayes’ Theorem
    Corresponding chapters in the textbook: Chapter 1
    Assignments: Assignment 1 (question 1 - 7)
  • Chapter 2: Random Variables
    • Chapter 2.1: Random Variables
      • Random Variables (RVs)
      • Cumulative Distribution Function (CDF)
      • Probability Density Function (PDF)
      • Continuous-type Random Variables: Normal (Gaussian), Uniform, Exponential, and Rayleigh RV
      • Discrete-type Random Variables: Bernoulli, Binomial, Poisson, Uniform, and Geometric RV
    • Chapter 2.2: Statistics of RVs
      • Mean (Expected Value)
      • Variance of a RV
      • Moments and Characteristic Function (CF)
      • Chebychev Inequality
      • Functions of a Random Variable
    Corresponding chapters in the textbook: Chapter 2 and Chapter 3
    Assignments: Assignment 1 (question 8 - 11); Assignment 2 (question 2 - 12); Assignment 3 (question 1, 2, 3, 12, 13).
  • Chapter 3: Two Random Variables
    • Chapter 3.1: Distribution Functions of Two RVs
      • Joint PDF
      • Marginal PDF
      • Independence of RVs
      • Functions of RVs
    • Chapter 3.2: Correlation, Covariance, Moments and CF
      • Correlation and Covariance
      • Joint Characteristic Function
      • Independence
    • Chapter 3.3: Gaussian RVs and Central Limit Theorem
      • Jointly Gaussian RVs
      • Central Limit Theorem
    • Chapter 3.4: Conditional Probability Density Functions
    • Chapter 3.5: Conditional Mean
      • Conditional Mean
      • Computing Expectation by Conditioning
      • Computing Probability by Conditioning
    Corresponding chapters in the textbook: Chapter 4 and Chapter 6
    Assignments: Assignment 2 (question 1); Assignment 3 (question 4, 6 - 11, 14); Assignment 4 (question 1- 6, 11-17)
  • Chapter 4: Stochastic Processes
    • Definition and Types of Stochastic Processes
    • Independent, Identically Distributed Random Sequences
    • Expected Value, Autocovariance, and Autocorrelation of a Stochastic Process
    Corresponding chapters in the textbook: Chapter 10
    Assignments: Assignment 3 (question 5)
  • Chapter 5: Markov Chains
    • Markov Property
    • Classification of States
    • Chapman-Kolmogorov Equation
    • Steady-State Probabilities
    • Mean time in Transient States
    Corresponding chapters in the textbook: Chapter 12
    Assignments: Assignment 4 (question 7-10); Assignment 5 (question 7, 8)
  • Chapter 6: Exponential Distribution and Poisson Process
    • Exponential Distribution
    • Poisson Process
    • Composing and Decomposing Poisson Processes
    • Racing Poisson Processes
    Corresponding chapters in the textbook: Chapter 10
    Assignments: Assignment 5 (question 1-6, 9)

 

 LECTURE NOTES

  • Course Overview, download
  • Chapter 1: Experiments, Models, and Probabilities, download
  • Chapter 2: Random Variables, download
  • Chapter 3 : Two Random Variables, download
  • Chapter 4 : Stochastic Processes, download
  • Chapter 5 : Markov Chains, download
  • Chapter 6: Exponential Distribution and Poisson Process, download

 

 ASSIGNMENTS

 

 QUIZ SOLUTION