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
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