Stanford University

## Fall Quarter 2022-2023

## Instructor: Kabir Chandrasekher; kabirc [at] stanford [dot] edu

## Lectures: TBD

## Description

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.

Axioms of probability, conditional probability, Bayes rule, independence

Random variables

Applications: Signal detection, parameter estimation, classificationExpectation, conditional expectation

Applications: Linear and nonlinear MSE estimation, quantizationInequalities and limit theorems, confidence intervals

## Reading

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

Lecture videos from Spring 2021

## Prerequisites

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

## Credit

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

Fulfills

Part of EE undergraduate core requirements

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

Prerequisite to many graduate courses

### Requirements

Weekly homework sets: 60%

Five quizzes: 20%

Final: 20%