2025 Fall

Prof. Youjian (Eugene) Liu

Why

• The course provides essential tools for understanding, modeling, and designing physical systems with uncertainty, such as sensors, communication and control systems, and robots. It lays the foundation not only for using but also for understanding and designing machine learning and artificial intelligence (ML/AI), including Markov processes in Reinforcement Learning (RL) and stochastic dynamics in diffusion models, which underlie most state-of-the-art image and video generative AIs. Additionally, it prepares students for other courses, including five AI/ML related courses, offered by the Machine Learning, Information Theory, Network, Communication, and Data Sciences (LINCD) group, https://www.colorado.edu/communications-data-science/courses.

Syllabus

• probability_ecen_5612_syllabus.pdf

• Canvas Course Site for quiz/homework submission and solution posting

Course Content (viewable with your CU account)

• All Lecture Notes in onenote

• Lecture Videos

• Homework Solutions: Under \Files on Canvas.

• Other notes: 

  • Prof. Gallager's notes on circularly symmetric complex Gaussian random variables

Homework (Due every Thursday: Upload to Canvas)

• 1. (Chapter#.problem#)  1.4, 1.24, 1.26, 1.29, 1.30, 1.31

  2. 1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.60

  3. 1..64, 1.70, 1.78, 2.9, 2.13, 2.15, 2.17

  4. 2.18, 2.34, 4.1, 4.7, 4.24, 5.13, 5.17, 5.18

  5. 2.38, 2.46, 3.22, 3.29, 3.42, 4.38, 4.48, 4.55

  6. 4.67, 5.37, 5.42 (d), 5.50,  5.55, 7.20, 7.27

  7. 8.7, 8.10, 8.22, 8.30, 9.5, 9.23, 10.1, 10.5

  8. 10.7, 10.8, 10.11, 10.26, 10.35, 10.38, 10.44, 10.51

  9. 11.3, 11.6, 11.9, 11.10, 11.14, 11.21, 11.25, 11.27

  10. 12.2, 12.6, 12.9, 12.23, 12.31, 13.1, 13.2

  11. 13.29, 13.30, 13.31