Syllabus
EE 503: Probability for Electrical and Computer Engineers
Summer 2026 (4 units)
This course focuses on reasoning with probabilistic uncertainty. This involves developing careful skills in logical reasoning and applying those skills to a wide range of problems in probabilistic and statistical inference from signal processing to machine learning. The course depends primarily on lecture material and handouts. Attendance is mandatory. There are weekly exams and no make-ups. Unexcused absences or early departures result in an automatic exam score of zero.
Lecture: Monday (section: 30401, 30403), 12:00 – 16:10
Discussion: Friday (section: 30402, 30404), 10:00 – 10:50
Enrollment is in-person and DEN ONLY. Attendance is mandatory to all lectures. Taping or recording lectures or discussions is strictly forbidden without the instructor’s explicit written permission.
Course materials
NOTE: Texts are secondary to in-class lecture material and homework sets.
Required: Probability and Random Processes for Electrical and Computer Engineers, Gubner, J.A., Cambridge University Press, 2006.
Required: Probability, Statistics, and Random Processes for Electrical Engineering, Leon-Garcia, A., Pearson, 2008.
Recommended: Computer Age Statistical Inference: Algorithms, Evidence, and Data Science, Efron, B., and Hastie, T., Cambridge University Press, 2016.
“No AI” policy
The use of AI tools is strictly prohibited and considered a serious violation of academic integrity. This includes all artificial intelligence technologies, including but not limited to large language models, text generators, and AI-assisted writing software, for any aspect of coursework — be it research, outlining, drafting, editing, or proofreading. Any suspected use of AI will be thoroughly investigated. Violations may result in severe consequences, including course failure and referral to the Office of Student Judicial Affairs and Community Standards for further disciplinary action.
Course Outline
| Week | Topics |
|---|---|
| 25 May | No class, Memorial Day. |
| Week 1 27 May |
Logic and sets. Proof technique. Sigma-algebras. Probability axioms. |
| Week 2 01 Jun |
Uncountability. Borel sigma-algebra. Independence. Total probability. |
| Week 3 08 Jun |
Combinatorics. Limits of sequences and sets. Borel-Cantelli Lemma. |
| Week 4 15 Jun |
Discrete probability and approximations. Poisson Theorem. |
| Week 5 22 Jun |
Random variables. Continuous densities. Bayes conjugate inference. |
| Week 6 29 Jun |
Expectations and moments of random variables. |
| Week 7 01 Jul |
Covariance. Correlation. Uncertainty principles. |
| Week 8 06 Jul |
Stochastic convergence. Laws of large numbers. |
| Week 9 13 Jul |
Conditional expectations. S.I.T. technique. Maximum likelihood estimation. |
| Week 10 20 Jul |
Transformed densities. Monte Carlo. Entropy and information. Mixtures. |
| Week 11 27 Jul |
Central limit theorem. Confidence intervals. Queues. |
| Week 12 03 Aug |
Discrete time Markov processes. Optimal estimation and least squares. |
| Monday 10 Aug |
Final, 12:00 - 14:30 |
Grading Procedure
Class grade depends on weekly exams and the final exam. Homework problems are optional. Homework handouts count as extra credit. Homework problems from the text do not count.
Weekly Exams (60%)
60 Points. 11 weekly exams. Closed book. 10 minutes at the start of each Monday lecture (and Wednesday on week 7). No make-up exams. Each weekly exam is worth 6 points. Missed exams earn 0 points. The total weekly exam score sums your 9 best weekly exam scores. Algorithm: label your weekly exam scores from lowest to highest: \(w_1 \le \cdots \le w_{11}\). Then \(W = 6 + w_{3} + \cdots + w_{11}\) is your total weekly-exam score. Synchronous class attendance is mandatory. Unexcused absences get an automatic exam score of zero for that week’s exam grade.
Final Exam (40%)
40 Points. Cumulative. The final exam is closed book with no notes sheet. You are expected to bring a non-graphing scientific calculator.
Homework
Textbook problems are checked but not graded. Handout problems are graded but count only as extra points. They count at most as 10 points if all homework sets turned in and accurately worked. Your grade remains as is if only some homework turned in. How much homework affects which cases is at the discretion of the instructor. You may discuss homework problems with classmates but each student must submit their own original work. Turning in identical homework sets counts as cheating. Cheating warrants an F in the course.
Course Grade
A if 90.00 - 100 points,
B if 80.00 - 89.99 points,
C if 70.00 - 79.99 points,
D if 60.00 - 69.99 points,
F if 0 - 59.99 points.
(“+” and “–” at ≈ 2.5% of grade boundary).
Cheating
Cheating is not tolerated on homework or exams. Penalty ranges from F on exam to F in course to recommended expulsion.