T RYERSON UNIVERSITY
Department of Electrical and Computer Engineering
EE8103 – Random Processes - Fall 2011
Course Information 

Last Updated on: Nov. 28, 2011

ANNOUNCEMENTSU

  • Quiz-4 solution has been posted. (Nov. 28, 2011)
  • Quiz-3 solution has been posted. (Nov. 15, 2011)
  • Mid-term exam solution has been posted. (Nov. 04, 2011)
  • Mid-term exam is scheduled at 6 PM on Oct. 27 in VIC 104. You are allowed to bring a calculator and one A4 double-sided formula sheet. There are total 6 questions, which are uniformly distributed from chapter 1 to chapter 3.3. (Oct. 23, 2011)
  • Quiz-2 solution has been posted. (Oct. 17, 2011)

  • Quiz-1 solution has been posted. (Sep. 30, 2011)

  • The first lecture will be held on Sep. 15, 2011. Please print the lecture notes (shown below) and bring them to the class.

     

UINSTRUCTOUURU

 

Dr. Yifeng He

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

U

 

LECTURE HOURS, ROOM, CONSULTING HOURSU

  • Lectures: Every Thursday, 6-9 PM, at VIC 104
  • 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, which are posted on the course website. Although the assignments are not collected, it is highly suggested students do the assignment questions 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.

 

U

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 (questions 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 (questions 8 - 11); Assignment 2 (questions 2 - 12); Assignment 3 (questions 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 (questions 4, 6 - 11, 14); Assignment 4 (questions 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
    Corresponding chapters in the textbook: Chapter 12
    Assignments: Assignment 4 (questions 8-10); Assignment 5 (questions 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 (questions 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