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  • Syllabus

    ECE528: Introduction to Random Processes in ECE

    Spring 2016

    Instructor: Zhi Gerry Tian

    Teaching Assistant: Venkata S. Veeramachaneni

    Class Meetings: Lectures (CRN 11333) -- W 7:20pm-10:00pm, Music Theater Building (MTB) 1004

    Recitation (CRN 11485) -- M 5:55pm-7:10pm, Robinson Hall (R) B102

    Office Hours: Wednesdays 4-6pm, Mondays 3:00-4:30pm; @ Nguyen Engineering Building Room 3242

    TA Office Hours: Mondays 7-8pm; and Fridays 4-5pm @ENGR 3204

    Course website:

    Notes, home assignments and other course materials will be posted on Blackboard

    Class announcements such as schedule changes and problem discussions will be posted via Blackboard. Each student is responsible for keeping up with the posted announcements.

    Textbook: Introduction to Probability, Second Ed.

    by Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2008. ISBN 978-886529-23-6

    Supplemental books:

    Probability, Statistics, and Random Processes, 3rd Edition

    by Alberto Leon-Garcia, Pearson Prentice Hall, 2008.

    Probability, Random Variables, and Stochastic Processes, 3rd Edition

    by Athanasios Papoulis, McGraw-Hill Inc, 1991.

    Prerequisites: ECE 220 and STAT 346, or permission of instructor. Ability to think clearly and formulate simple mathematical proofs is essential.

    Be ready to pick up some basic MATLAB skills.

    Course Description: This course develops the mathematical theory of probability, random variables and

    random processes for Electrical Engineers. The goal is to teach the basic theoretical concepts and

    techniques for solving problems that arise in practice, with focus on statistical techniques as applied to the

    study of random signals and noise. Beginning with the Axioms of Probability, this course introduces the

    assignment of probability laws to discrete and continuous sample spaces, which leads to the concept of

    random variables, pairs of random variables and finally random processes. Topics include random

    variables and their functions; random processes in continuous and discrete time and space; stationarity

    and ergodicity vectors; expectation and variance; conditional expectation; moment-generating and

    characteristic functions; random processes such as white noise and Gaussian; second-order properties of

    random processes such as autocorrelation and power spectral density; interaction of random processes

    with linear systems; linear filtering of random processes; and basic ideas of estimation and detection.

    These concepts and techniques prepare students for advanced study of topics in electrical and computer

    engineering, such as communication theory, signal and image processing, remote sensing, control theory,

    discrete-event systems, and computer networks.

    Requirements: Weekly homework assignments, quizzes, in-class midterm exams*, and final exam.

    Attendance is expected. Students are responsible for all assigned readings, class lectures, as well as material

    covered in class that is not in the book.

  • Homework Assignments: All homework assignments are due in class on the specified due date, with no late

    assignments accepted.

    Grading Policy: homework and quizzes 20%; mid-term 1 15%; mid-term 2 30%; final exam 35%. * When mid-term 1 is cancelled, the grading is: homework and quizzes 20%; mid-term 35%; final exam 45%.

    Course Outline and Schedule (subject to change)

    1. Review of Probability: 1.1. Set Thory, Probability Spaces; 1.3 Conditional Probability and Independence

    2. Random Variables: 2.1 Basic Concepts; 2.2 Distribution, Density, and Mass Functions; 2.3 Functions of

    Random Variables; 2.4 Expectations, Moments, and Characteristic Functions

    3. Pairs of Random Variables: 3.1 Joint and Marginal Distributions; 3.2 Conditional Distributions and

    Independence; 3.3 Functions of Two Random Variables; 3.4 Expectations and Correlations

    *** MIDTERM EXAM 1 (Feb. 17 or 24) Cancelled ***

    4. Random Vectors: 4.1 Joint, Marginal, and Conditional Distributions; 4.2 Functions of

    Several Random Variables; Expectations and Correlations; 4.3 The Multivariate Gaussian Distribution

    5. Sequences of Random Variables; Convergence Concepts;

    Law of Large Numbers and Central Limit Theorem

    ***REVIEW *** MIDTERM EXAM 2 (March 23) ***

    6. Stochastic Processes

    6.1. Basic Concepts

    6.2. Covariance, Correlation, and Stationarity

    6.3. Gaussian Processes and Brownian Motion

    6.4. Poisson and Related Processes

    6.5. Power Spectral Density

    6.6. Stochastic Processes and Linear Systems

    7. Introduction to Markov Chains

    7.1. Markov Processes

    7.2. Markov Chains

    *** FINAL EXAM (early May) ***

    Course and University Policies

    Honesty and Integrity: Mason expects students to pursue their academic work with honesty and integrity. Students should feel free to work in groups to discuss lecture material and homework

    assignments; however, under no circumstance should a student represent anothers work as his or

    her own. Copying solutions for assigned homework problems, from any source, constitutes a violation

    of the university honor code. Any forms of cheating may cause penalties, from getting F in this course

    to academic actions in accordance with university policy.

    Email Communications: Students must use their MasonLive email account to receive important University information, including messages related to this class. See for more

    information. Homework assignments and other course material will be emailed to your MasonLive

    email account. Also, when you send me an email, please write ece528 on the subject line.

    University Policies: The University Catalog,, is the central resource for university policies affecting student, faculty, and staff conduct in university academic affairs. Other

    policies are available at All members of the university community are

    responsible for knowing and following established policies. Academic integrity is of great importance to

    the Mason community. Mason provides accommodations through the Office of Disability Services.


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