Lecture

Probability and Statistics for SIC

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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 the fundamental concepts of probability and statistics, focusing on random experiments, probability spaces, random variables, and statistical inference. Examples include tossing a coin, rolling dice, and calculating probabilities in different scenarios. The lecture also explores event spaces, sigma-algebras, and the likelihood of various outcomes. The instructor provides insights into the mathematical modeling of random experiments and the calculation of probabilities in different contexts.

Instructors (2)

Raphaël Jean Berthier

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

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Mathematics

Probability theory: Topics in probability theory

Related concepts (32)

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

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.

Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).

Sample space

In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.

Complex random variable

In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.

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