EE 520, Fall 2026

Random Processes

This is the course website for EE 520, Random Processes, Fall 2026 quarter.

Meeting time: Mon/Wed 3:30-5:10PM, FAB 171
Office hours: Mon/Wed 5:10-6:10PM (or by appointment), FAB 160-19

Course Description

The goal of this course is a rigorous, application-driven understanding of probability and random processes at the graduate level. One idea organizes the entire quarter: a probability model answers three questions — what is uncertain, what is observed, and how should observation change belief and action? We apply that one formula to progressively bigger objects: a single hidden fact, one random variable, a pair, a Gaussian vector, and finally an entire function.

The course runs in five movements:

  1. Belief and conditioning (sessions 1–3) — probability as the calculus of belief, Bayes’ rule as a learning algorithm, acting on a posterior
  2. One random variable (sessions 4–7) — discrete and continuous models, extremes, transformations, sampling, and the value of a measurement
  3. Two random variables (sessions 8–11) — joint structure, conditional expectation, detection, and learning a probability (Beta–Bernoulli and bandits)
  4. Gaussian vectors and linear estimation (sessions 13–15) — covariance as geometry, Gaussian conditioning, LMMSE and sensor fusion
  5. Processes: the same formula, infinite index (sessions 16–19) — Gaussian processes, stationarity as kernel structure, LTI systems and the Wiener filter, and adaptive sampling

Textbook: The course will use the free textbook below.

Syllabus: Course Syllabus.

Communication: I will not use email for course communication. All written questions should be posted to the appropriate channel on the Slack workspace (see Homework 0).

Course Schedule

Two 100-minute sessions per week for ten weeks: 18 lecture sessions plus a midterm and final. Sessions open with a motivating application or live demo, develop the theory rigorously, and close by converting a posterior into a decision. Assignments are typically due Fridays at 11:59PM.

Fall 2026 course schedule for EE 520
Date Lecture Topic Sections Assignment Due (Friday)
9/28 1 why probability? search and belief 1.1-1.4 ---
9/30 2 Bayes' rule and sequential updating 1.5-1.7 ---
10/5 3 independence, conditional independence, and acting on belief --- ---
10/7 4 discrete random variables 2.1-2.4 HW1 due Fri 10/9
10/12 5 named models and extremes 2.4, 3.4, 3.5 ---
10/14 6 continuous random variables 4.1-4.4, 5.1 HW2 due Fri 10/16
10/19 7 functions of one RV, sampling, and the value of a measurement 5.2-5.5 ---
10/21 8 joint structure 7.1-7.5 ---
10/26 9 conditional expectation 3.3, 8.4 ---
10/28 10 detection 8.4-8.6 HW3 due Fri 10/30
11/2 11 Bayes with a continuous parameter; bandits; midterm review --- ---
11/4 12 random vectors and covariance 8.1-8.3 HW4 due Fri 11/6
11/9 --- MIDTERM EXAM (covers Lectures 1-10, HW 1-4) --- ---
11/11 --- NO CLASS (Veterans Day) --- ---
11/16 13 Gaussian vectors and conditioning 9.1-9.5 ---
11/18 14 LMMSE, orthogonality, and fusion 8.4-8.6 HW5 due Fri 11/20
11/23 15 Gaussian processes 11.1-11.4 ---
11/25 16 WSS: stationarity as kernel structure 10.1-10.4 HW6 due Fri 11/27
11/30 17 constructing processes: LTI systems and the Wiener filter 10.5-10.8 ---
12/2 18 capstone: adaptive sampling, and the course in one formula --- HW7 due Fri 12/4

Lecture Notes

Assignments

All assignments must be submitted via the course assignment platform to obtain credit. See Homework 0 below for information on how to set up an account.

I provide the \(\LaTeX\) file used to generate each homework below. You must use this as a template to receive extra credit.

Note the two hard due dates: HW2 is due at the start of session 6 and HW7 at the start of session 19 — several in-class payoffs (the first-alarm example, the adaptive-sampling demo) assume the corresponding work has already been submitted.

Resources