Course

MATH-432: Probability theory

Summary

The course is based on Durrett's text book Probability: Theory and Examples.
It takes the measure theory approach to probability theory, wherein expectations are simply abstract integrals.

Lectures

Instructor

Thomas Mountford

Teaching & PhD Past EPFL PhD Students Damien Gauthier, Samir Brahim Belhaouari, Driss Baraka, Daniel Rodrigues Valesin, Samuel Schöpfer, Kamran Kalbasi, Jacques Saliba, Hao Xue, Keming Chen Past EPFL PhD Students as codirector Guillaume Charles Woessner Courses Analysis I MATH-101(d) Study the fundamental concepts of analysis, and the differential and integral calculus of real-valued functions of one real variable. Markov chains MATH-332 The course follows the text of Norris

Official source

https://edu.epfl.ch/coursebook/en/probability-theory-MATH-432

Moodle Page

http://go.epfl.ch/MATH-432

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Summary

The course is based on Durrett's text book Probability: Theory and Examples.
It takes the measure theory approach to probability theory, wherein expectations are simply abstract integrals.

Lectures

Instructor

Thomas Mountford

Official source

https://edu.epfl.ch/coursebook/en/probability-theory-MATH-432

Moodle Page

http://go.epfl.ch/MATH-432

About this result

Lectures in this course (28)

Introduction and Probability Spaces

Covers the basics of probability theory, including probability spaces and random variables.

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Characteristic Functions: Definition and Properties

Covers characteristic functions for random variables and their properties, including independence and convergence.

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

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