Cleveland State University
Department of Electrical Engineering and Computer Science
EEC 512 Probability And Stochastic Processes
Catalog Data:
EEC 512 - Probability and Stochastic Processes(4 credits)
Prerequisite(s): Graduate standing.
General concepts of probability and random variables, including random
experiments, inequalities, joint distributions, functions of random variables,
expectations, and the law of large numbers. Basic concepts of random processes and
their properties are introduced. Markov process, linear systems with stochastic
inputs, and power spectra are presented.
Textbook:
Probability, Random Variables, and Stochastic Processes, by Athanasios Papoulis,
Fourth Edition, McGraw Hill, 2004.
References:
 An Introduction to Probability and Stochastic Processes, by James L. Melsa and
Andrew P. Sage, Prentice Hall, 1973.
 Introduction to Random Processes, by William A. Gardner, Second Edition,
McGraw Hill, 1990.
 Probability and Random Processes for Electrical Engineering, by Alberto LeonGarcia, Addison-Wesley, 1989.
 Digital Modulation Techniques, by Fuqin Xiong, Artech House, 2000
Instructor:
Dr. Murad Hizlan,
Office: FH338,
Tel: 216-687-4526
Email: m.hizlan@csuohio.edu
Course Objectives:
This course introduces students to probabilities, random variables, and stochastic
processes. At the end of this course, the students should understand probabilistic
space, events and their probabilities, random variables and their probability
densities, functions of random variables, expectations, correlation functions and
power spectral densities of stochastic processes, and their applications. The students
also should be able to derive or compute probabilities, densities, expectations,
correlations, and power spectral densities. This course provides the fundamental
background for communications, computer communications networks, controls, and
signal processing.
Grading Policy:
Midterm Test I: 30%,Midterm Test II: 30%, Final Exam: 30%, Homework 10%.
Remarks:
As graduate students you are required to read the text before the lecture and after the
lecture.Homework will be assined and graded. Answers will be provided.
Course Outline:
Session
Topics
Reading (sections)
1-1 to 1-3, 2-1,2-2
25
The meaning of probability, set theory,
probability space, probability axioms
Conditional probability, Baye’s theorem,
independence
Labor Day (Sept.-1)
Bernoulli trails, binomial distribution,
Demoivre-Laplace Theorem
The law of large numbers, Poisson theorem
and random points
Random variables, distribution and density
functions,
Important densities, conditional
distributions
Function of one random variable,
fundamental theorem, examples
Mean and variance, moments, characteristic
function
Review
Midterm Test I
Two random variables, joint distribution
and density, probability mass
One function of two random variables
Two functions of two random variables,
applications
Continuing discussion of functions of two
random variables: joint moments,
correlation, independence, joint
characteristic function
Conditional distributions, Baye’s theorem,
conditional expected values
Sequences of random variables,
independence, correlation matrix,
conditional densities
Stochastic convergence and limit theorems
Stochastic processes and their statistics
Correlation functions, stationary processes
Review
Midterm Test II
Systems with stochastic inputs, ergodicity
Spectra of stochastic processes,
Output of a linear system
Discrete-time processes
26
PSD of bandpass signals
27
PSD of baseband digital signals
Appendix A (F.
Xiong)
Appendix A (F.
Xiong)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2-3,
Assignments
22,4,8,9,12,14,17
3-1 to 3-3
3-3, 3-4
3-4,5,8,11,12,13
4-1, 4-2
4-3,4-4
4-4,8,9,12,19,20
5-1 to 5-2
5-3 to 5-5
51,2,18,21,22,26
Chapters 1 to 5
6-1
6-2
6-3
6-2,4,6,7,8,9
7-1,7-2
7-3,7-4
7-1,3,4,7,8,16
8-1,8-2
8-4, 8-5
10-1
10-1
8-4,5,12,30,31
Chapters 6 to 8,10-1
10-2
10-3
10-4
101,3,22,27,33,35,
41
28
PSD of digitally modulated carrier signals
29
PSD of digitally modulated carrier signals
(continue)
FINAL EXAM
30
Appendix A (F.
Xiong)
Appendix A (F.
Xiong)
Chapters 10 and PSD
Note: Class starts at 8-25 and ends on 12-3 (Wed.). Final exam is on 12-8 (Mon.) There are total of 15
weeks for classes. September 1 (Mon.) is Labor day, a University holiday. So there are a total 29 class
times.