Fall 2024 - EE 381J Probability and Stochastic Processes I

Meets TuTh 9:30-11am 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
Convergence and Limit Theorems for 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.
Random processes: Definition and examples of discrete and continuous random processes: IID RVs, random walk, independent increment processes, Poisson process, Gaussian processes. Stationarity and ergodicity, correlation functions, continuity, differentiation, and integration of random processes. White noise, bandlimited processes. Response of linear systems to random inputs.
Markov Chains: Discrete Time Markov Chains, structural properties, stationary distribution, positive/null recurrence, transience, convergence to stationary distribution, ergodicity,reversibility
Martingales: Examples, Martingale Convergence Theorem, Online Stopping Theorem, Azuma-Hoeffding Inequality

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

Introduction to Probability, Dimitri Bertsekas and John Tsitsiklis. ( I teach out of this for my undergraduate class)
Random Processes for Engineers, B. Hajek, December 2015. (You can download this book from the web )
Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues, P. Bremaud., Online version available from UT Online library (https://www.lib.utexas.edu/)
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 through the Canvas course webpage.
We will use Ed for shared online question & answer and discussions. You can access Ed 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 tentative dates for the exams are below:

Midterm 1, scheduled for Thursday October 3 in class
Midterm 2, planned for November 7 in class
Final scheduled for Friday December 13th, 10:30am-12:30pm

No make-up 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. 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. For a start you should make sure to introduce 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, 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 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 471-6259, 471-4241 TDD or the College of Engineering Director of Students with Disabilities at 471-4321.