Probability Theory
You are on the course page for Probabilities, taught at Level L2 (second year) in the Economics and Management track of the Faculty of Economics and Management at Aix-Marseille Université. This course is intended for students enrolled in the International Program in Business in Economics track.
The “Extra” column for Chapter 6 links to a Shiny app to visualize a few probability distributions.
Upon completion of the course, students will be able to work with basic probabilistic models, analyse random variables, and understand key notions of convergence upon which statistical and econometric methods are based.
Goal
The goal of this course is to lay the foundations of probability theory. We will introduce the fundamental concepts and tools needed to understand randomness, quantify uncertainty, and model real-world phenomena. Students will learn how probabilistic reasoning can be applied in economic and social contexts.
Outline
- Sets, Random Experiments, and Combinatorics
- Basic Probability Theory
- Random Variables
- Pairs of Random Variables
- Asymptotic Convergence
Keywords
Probability theory; Combinatorics; Probabilistic models; Random variables; Joint distributions; Moments; Independence; Conditional probability; Law of large numbers; Asymptotic convergence.
Logistics
The course consists of 10 classes, each lasting 3 hours.
Reading Materials
Lecture notes are provided and are sufficient to cover the entire course. No single textbook is mandatory.
Students wishing to deepen their understanding may consult the following references as complementary readings:
- Hansen (2022)
- Newbold, Carlson, and Thorne (2023)
- Blitzstein and Hwang (2019)
- McClave, Benson, and Sincich (2022)
An excellent reference (in French), with numerous solved exercises:
- Elsner Bernhard (2021)
Prerequisites
Students are expected to be familiar with:
- Basic calculus (functions, limits, derivatives, integrals),
- Introductory linear algebra.
No previous background in probability is required. All fundamental concepts will be introduced during the course.
The first version of this course was created in French by Mathieu Faure, who kindly shared his teaching materials.