Lecture

Combinatorial Mathematics

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In course

MATH-232: Probability and statistics (for IC)

Cours d'introduction à la théorie des probabilités et aux statistiques. ...

Description

This lecture covers topics in combinatorial mathematics, including permutations, combinations, binomial coefficients, and multinomial coefficients. The instructor explains the properties of binomial coefficients and demonstrates their applications in various scenarios. The lecture also delves into the concept of partitions of integers and the exponential series. Additionally, it introduces a small lexicon of mathematical terms related to probability and statistics, such as sample space, event space, and probability distribution. The presentation concludes with a discussion on probability spaces and the independence of events.

Instructors (2)

Emmanuel Abbé

Teaching & PhD PhD Students Denys Pushkin, Ortal Yona Senouf, Vladyslav Shashkov Past EPFL PhD Students Elisabetta Cornacchia, Aryo Lotfi Courses Reasoning in artificial intelligence MATH-700 Large language models have raised the potential of artificial intelligence in various applications, including science and mathematics, but their reasoning capabilities remain under investigations. This class focuses on defining, measuring and improving the reasoning capabilities of such AI models. Awa

Raphaël Jean Berthier

Official source

Ontological neighbourhood

Mathematics

Probability theory: Topics in probability theory

Statistics

Statistical inference: Mathematical statistics

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Probability space

In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: A sample space, , which is the set of all possible outcomes. An event space, which is a set of events, , an event being a set of outcomes in the sample space. A probability function, , which assigns each event in the event space a probability, which is a number between 0 and 1.

Sample space

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Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

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