Lecture

Probability and Statistics

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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 various topics in probability and statistics, including moments, variance, and expected values. The instructor discusses the calculation of moments, the variance of random variables, and the expected number of trials to achieve a specific outcome. Pascal's triangle is used to simplify calculations and understand the distribution of tokens in a product. The lecture also explores the concept of entropy and maximal variance in probability theory.

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

Related concepts (32)

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Aerobic exercise

Aerobic exercise (also known as endurance activities, cardio or cardio-respiratory exercise) is physical exercise of low to high intensity that depends primarily on the aerobic energy-generating process. "Aerobic" is defined as "relating to, involving, or requiring oxygen", and refers to the use of oxygen to meet energy demands during exercise via aerobic metabolism adequately. Aerobic exercise is performed by repeating sequences of light-to-moderate intensity activities for extended periods of time.

Health club

A health club (also known as a fitness club, fitness center, health spa, weight room and commonly referred to as a gym) is a place that houses exercise equipment for the purpose of physical exercise. In recent years, the number of fitness and health services have increased, expanding the interest among the population. Today, health clubs and fitness centers are a reference of health services, rising the adherence to physical activity.

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 axioms

The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .

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