EE 178: Probabilistic Systems Analysis

Stanford University

Spring Quarter 2021-2022

Instructor: Professor Abbas El Gamal; abbas [at] ee [dot] stanford [dot] edu

Lectures: TBD


Real-world phenomena and systems are probabilistic in nature: the outcome of an experiment is uncertain; when an input is applied to a system, the output is not predictable. Examples are all around us from gambling and the financial markets, sports, medical diagnosis and spread of disease, electronic devices, communication and storage systems, Internet traffic and social networks, renewable energy, polling and elections, climate and evolution, to statistical and quantum physical systems. The modeling and analysis of probabilistic systems involve the fields of probability theory, statistics, machine learning and statistical signal processing.

This course covers the basic concepts and techniques of probability theory with applications to statistics, machine learning and statistical signal processing. Examples and homework problems are drawn from many fields. To see probability in action and to demonstrate the process of probabilistic modeling and analysis, the homework sets include computational problems in Python, some with real data.

Topics include (see syllabus)

  • Axioms of probability, conditional probability, Bayes rule, independence

  • Random variables
    Applications: Signal detection, parameter estimation, classification

  • Expectation, conditional expectation
    Applications: Linear and nonlinear MSE estimation, quantization

  • Inequalities and limit theorems, confidence intervals


  • Lecture slides (will be posted on the Canvas class webpage)

  • Lecture videos from Spring 2021

Class website


Calculus at the level of MATH 51, CME 100 or equivalent (see Some Math for the level of math needed) and basic knowledge of computing at the level of CS106A


  • 4 units for undergraduate students; 3 units for graduate students; letter grade or CR/NC


  • Part of EE undergraduate core requirements

  • GER:DB-EngrAppSci, WAY-AQR, WAY-FR

  • Prerequisite to many graduate courses


  • Weekly homework sets: 60%

  • Five quizzes: 20%

  • Final: 20%