ECE 528:Introduction to Random Processes in ECE

Syllabus PDf: ECE 528 Syllabus

Course Number	ECE 528
Prerequisites	Prerequisites: ECE 220 and STAT 346 (all with grade of C or better), or permission of instructor.
Instructor:	Bijan Jabbari, Professor
Semester:	Fall 2020
Lecture Time:	Wednesday 7:20-10:00 pm
Location:	Online
Office:	Eng. Bldg. Room 3232
Office Phone:	703-993-1618 (use email only)
Email:	bjabbari@gmu.edu
Web:	http://cnl.gmu.edu/
Office Hours:	by appointment
Teaching Assistant:	Haotian Zhai (email: hzhai@gmu.edu)
Office Hours:	Monday and Wednesdays: 9:30-10:30 am
Administrative Assistant:	N/A
Course Description	Probability and random processes are fundamental to communications, control, signal processing, and computer networks. Provides basic theory and important applications. Topics include probability concepts and axioms; stationarity and ergodicity; random variables and their functions; vectors; expectation and variance; conditional expectation; moment-generating and characteristic functions; random processes such as white noise and Gaussian; autocorrelation and power spectral density; linear filtering of random processes, and basic ideas of estimation and detection.

Course Outline

Probability Models in ECE
Review of probability: set theory, basic concepts, probability spaces, conditional probability, Bayes’ Rule, independence, Borel Fields, Generation of random numbers
Discrete Random Variables: Notion of Random Variables, Probability Mass Functions (PMF), Expected Value and Moments, Important Discrete Random Variables, Generation of Discrete Random Variables
General Random Variables (Single Variable): Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), functions of random variables, expectations and characteristic function, Markov and ChebyShev inequalities
Pairs of Random Variables: joint and marginal distributions, conditional distributions and independence, functions of two random variables, Expectations and correlations, pairs of jointly Gaussian Random Variables, generating jointly Gaussian Random Variables
Random vectors: Functions of several random variables expected value of vector random variables, jointly Gaussian Random vectors, convergence of random sequences
Sums of random variables and long-term averages: the sample mean and the Laws of Large Numbers, the Central Limit Theorem
Stochastic Processes: Basic concepts, Covariance, correlation, and stationarity, Gaussian processes and Brownian motion, Poisson and related processes, Power spectral density, Stochastic processes and linear systems
Markov Processes and Markov Chains

Probability, Statistics, and Random Processes, 3rd Edition, by Alberto Leon-Garcia, Pearson Prentice Hall, 2008.
D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability. Athena Scientific, Belmont, MA, 2nd Edition, 2008. See http://www.athenasc.com/probbook.html

There will be weekly assignments, one Mid-term exam, and a Final exam. They will count towards the grade as follows: