Fall 2015 - EE 381J Probability and Stochastic Processes I
Meets TuTh 9:30-11am in WRW 113
Unique No: 16795
Gustavo de Veciana
Office: ACES 3.120
Office Hours: See my personal web page for updated times.
This course serves as an intermediate level course on probability
and stochastic processes for engineers. We will review concepts in
probability and stochastic processes introducing some of the measure theoretic
foundations and other techniques and concepts that may be of use
to you in subsequent courses and research. In addition we will discuss the
most common probabilistic models and random processes and introduce
basic techniques in estimation and detection, estimation,with a view on
important applications in communications, control and signal processing,
as well as other fields in engineering and computer sciences.
Review of basic probability:
probability spaces, random variables, distribution and density functions, expectation, characteristic functions, conditional probability, conditional expectation
Sequences of random variables: convergence concepts, laws of large numbers, central limit theorem, large deviations
random vectors, covariance characterization, jointly Gaussian random variables.
Estimation and detection:
Estimation, MAP, ML, orthogonality principle, minimum mean and squared
and linear least square error estimation. Detection, MAP, ML and
Basic concepts of random processes:
definition and classification, stationarity and ergodicity, correlation functions, continuity, differentiation, and integration of random processes
Representations of random processes:
sampling theorem, Karhunen-Loeve expansion, envelope representation and simulation of narrowband processes.
Markov processes, Martingales, Wiener process,
Poisson processes, shot noise, thermal noise, random walk.
This course is intended for first year engineering graduate students, you
must have had an undergraduate course in probability as well
as background signals and systems. In addition it will be very helpful if you
have taken an course where you have learned
formal proof techniques, e.g., real analysis, discrete math, or algorithms.
"Required" Text: Highly Encouraged
Probability and Random Processes, G.R. Grimmett and D.R. Strizaker,
Oxford, 3rd Edition. ( overall graduate level intro to probability)
Other Recommended Texts
Probability in Electrical Engineering and Computer Science: An Appication-
J. Walrand, Feb 2014.
(This text develops some nice applications motivating the need to learn
An Exploration of Random Processes for Engineers,
B. Hajek, December 2011.
(You can download this book from the
Stochastic Processes:Theory for Applications, R.G. Gallager 2012.
(You can download a draft of this book at
Introduction to Probability, Dimitri Bertsekas and John Tsitsiklis.
( I teach out of this for my undergraduate class)
Stochastic Processes, Sheldon Ross, Wiley.
Course web page
The course web pages will be on the Canvas system.
You need a UT-EID and password and must be registered for the course
to access the system. Course handouts, homeworks,
sample exams, and solutions will be made available via the course homepage.
It is your responsibility to check for homework
assignments each week. If you are auditing this course, you will
need a course buddy from which to get this material.
Homeworks will be assigned on the course web pages. The homeworks will be
due in class at the BEGININING of class, before the class starts.
You are expected to make an honest, independent attempt to solve
and turn in your answers to each homework question.
Late howeworks will be awarded a grade of zero unless permission is
sought in advance to turn in late and is based on a valid reason such as
a medical emergency. Nevertheless all homeworks must be turned in
to pass the course. It is your responsibility to check the course
homepage for homework assignements each week.
Midterm and Final Exams
There will be two midterms and a final in this class. Some estimated
dates and the locations of the exams are below:
No make-up exams will be given for the mid-terms.
Excused absence from an exam must be obtained
in advance. In this case the student's final exam grade will be substituted
for the missed exam. In the case of an excused absence from the final exam,
the course grade will be based on the homework and midterm exams.
Unexcused absences from a midterm or final will result in a grade of zero
for that exam. Note that excused absences from exams will be made only
in extreme circumstances (serious illness, death in the immediate family,
etc.). Requests for excused absences should be made in writing and must
be supported by appropriate documentation.
- Midterm 1, planned for September 24, in class
- Midterm 2, planned for November 3 or 5 in class
- Final will be Saturday December 12th, 9-12noon.
The final grade will be a weighted average of your homework, mid-term,
and final scores. The weightings are:
Class Participation: 5%
Midterm 1: 20%
Midterm 2: 25%
Where does this course fit in?
This course is intended as a broad introduction to provide a basis for
graduate study in the CommNetS Area. A sequel to this course, Probability
and Random Processes II, will delve into the area in more depth.. Additional
courses that you might consider taking after this one include: Communication
Networks: Analysis and Design ,Performance Evaluation; Digital
Signal Processing; Digital
Communications ;Wireless Communications; Advanced Signal Processing;
Theory. Randomized Algorithms.
Academic dishonesty and policies on cheating
Faculty in the ECE Department are committed to detecting and punishing
all instances of academic dishonesty and will pursue cases of academic
dishonesty in accordance with university policy. Academic dishonesty,
in all its forms, is blight on our entire academic community. All
parties in our community - professors, staff, and students - are responsible
for creating an environment that educates outstanding engineers, and this
goal entails excellence in technical skills, self-giving citizenry, and
ethical integrity. Industry wants engineers who are competent and
fully trustworthy, and both qualities must be developed day by day throughout
an entire lifetime.
Details about what constitutes academic dishonesty can be found at the
following URL: UT Dean of Students Office (http://www.utexas.edu/depts/dos/sjs/academicintegrity.html).
All cheating will be reported directly to the college/university. Unless
explicitly indicated in an assignment, you must do your homeworks, projects
and exams individually. You are welcome and encouraged to discuss
material with your colleagues, when and where it is appropriate,
but copying, stealing papers, etc. are considered dishonest and will be
Allegations of Scholastic Dishonesty will be dealt with according to
the procedures outlined in Appendix C, Chapter 11, of the General Information
The University of Texas at Austin provides, upon request, appropriate
academic adjustments for qualified students with disabilities. For more
information, contact the Office of the Dean of Students at 471-6259, 471-4241
TDD or the College of Engineering Director of Students with Disabilities