Introduction to Random Processes (ECE 440) is an entry-level graduate class that explores stochastic systems. The latter could be very loosely defined as anything random that changes in time, and the evolution of such systems is mathematically described by a random process. Stochastic systems are at the core of a number of disciplines in engineering, for example communication systems and machine learning. They also find application elsewhere, including social systems, markets, molecular biology and epidemiology, just to name a few.

Class objectives

The goal of the class is to learn how to model, analyze and simulate stochastic systems. With respect to analysis we distinguish between what we could call theoretical and experimental analysis. By theoretical analysis we refer to a set of tools which let us discover and understand properties of the system. Naturally, probability theory plays a key role as the mathematical language that allows us to quantify uncertainty. The theory can only take us so far and is usually complemented with numerical analysis of experimental outcomes. Although we use the word experiment more often than not we simulate the stochastic system in a computer and analyze the outcomes of these virtual experiments.

Class information

When: Mondays and Wednesdays 4:50-6:05 pm.
Where: Goergen Hall 109.
Textbook: We will use lecture slides to cover the material. The basic textbook for the class is

  • John A. Gubner, "Probability and Random Processes for Electrical and Computer Engineers," Cambridge University Press.

The book can be obtained online from the University of Rochester libraries here.

An additional good reference for topics including Markov chains, continuous-time Markov chains, and queuing models is

  • Sheldon M. Ross, "Introduction to Probability Models," 11th ed. (earlier editions are fine), Academic Press.

Both books are on reserve for the class in Carlson Library, and are also available from the University of Rochester Bookstore.

Prerequisites: Useful to have good background in Probability Theory (of which we will do a fast-paced review the first five lectures), as well as Calculus and Linear Algebra (i.e., integrals, limits, infinite series, differential equations, vector/matrix notation, systems of linear equations, eigendecomposition). For homework assignments we will use Matlab (which can be obtained following these instructions); see the user guide here.

Credit distribution: Homework assignments (~10, 28 points), in-class midterm (Nov. 6, 36 points), take-home final (Dec. 10-13, 36 points).
Grading: At least 60 points are required for passing (C grade), a B requires at least 75 points, and an A at least 92. Undergraduate (ECE 271) students are expected to complete the same assignments and exams, but will be awarded extra 10 points counting towards the final grade.

Instructor: Gonzalo Mateos
Office hours: Tuesdays 10am, 413 Hopeman Engineering Building.
Teaching assistants and office hours: Rasoul Shafipour, Yang Li and Chang Ye.

  • Mondays 1pm, 414 Hopeman Engineering Building (Chang).
  • Thursdays 3pm, 412 Hopeman Engineering Building (Rasoul).
  • Fridays 1pm, 412 Hopeman Engineering Building (Yang).