Fall 2024  EE 381J Probability and Stochastic Processes I

Meets TuTh 9:3011am in CPE 2.210

Unique No: 17985
Instructor

Gustavo de Veciana

Office: EER 6.874

Office Hours: See my personal web page for updated times.

Email: gustavo@utexas.edu

WWW: http://www.ece.utexas.edu/~gustavo
Description
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,with a view on
important applications in communications, control and signal processing,
machine learning, as well as other fields in engineering and computer sciences.
Lecture Plan

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:
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
Bayesian criteria.

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, KarhunenLoeve expansion, envelope representation and simulation of narrowband processes.

Special processes:
Markov Chains, Martingales, Wiener process,
Poisson processes, shot noise, thermal noise, random walk.
Prerequisites
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
An Exploration of Random Processes for Engineers,
B. Hajek, December 2011.
(You can download this book from the
web )
Stochastic Processes:Theory for Applications, R.G. Gallager 2012.
(You can download a draft of this book at
web )
Introduction to Probability, Dimitri Bertsekas and John Tsitsiklis.
( I teach out of this for my undergraduate class)
Probability in Electrical Engineering and Computer Science: An Appication
Driven Course,
J. Walrand, Feb 2014.
(This text develops some nice applications motivating the need to learn
this material.)
Stochastic Processes, Sheldon Ross, Wiley.
Course web pages
 Class materials and homeworks will be posted on Canvas (Use your UT eid to sign in)
 Homeworks will be submitted on Gradescope.
You can access Gradescope Piazza through the Canvas course webpage.

We will use Piazza
for shared online question & answer and discussions.
You can access Piazza through the Canvas course webpage.
Homeworks
Homeworks will be assigned on Canvas. They will be
submitted and graded via Gradescope. Gradescope and/or other
regrade requests for homeworks/exams must be submitted within 1 week of their return.
You are expected to make an honest, independent attempt to solve
and turn in your answers to each homework question.
No late homeworks will be accepted. To allow some flexibility if you
have a problem some week, the two lowest homework scores will be dropped.
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:
 Midterm 1, planned for October in class
 Midterm 2, planned for November in class
 Final will be Friday December 13th, 10:30am12:30pm /li>
No makeup midterm exams will be given.
An excused absence for a midterm must be obtained in advance.
If you obtain an excused absence for a midterm your final exam grade will be substituted
for the missed midterm 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.
Exams will be graded on gradescope, Gradescope and/or other
regrade requests on exams must be submitted 1 week after their return.
Grading policy
The final grade will be a weighted average of your homework, midterm,
and final scores. The weightings are:
Class Participation: 5%
Homeworks: 20%
Midterm 1: 20%
Midterm 2: 25%
Final: 30%
Class participation is evaluated in several ways. Have you introduced yourself
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, selfgiving 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
prosecuted.
Notes:
Allegations of Scholastic Dishonesty will be dealt with according to
the procedures outlined in Appendix C, Chapter 11, of the General Information
Bulletin, http://www.utexas.edu/student/registrar/catalogs/.
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 4716259, 4714241
TDD or the College of Engineering Director of Students with Disabilities
at 4714321.