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Lecture

Multivariate Normal Distribution

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 multivariate normal distribution, including the definition, properties, and applications. It explains how to find the mean vector and covariance matrix, the moment-generating function, and the characteristic function. The lecture also delves into the Cartesian product of sets, combinatorics, and linear combinations of normal variables.

Instructors (2)

Raphaël Jean Berthier

Emmanuel Abbé

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Characteristic function (probability theory)

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Moment-generating function

In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables.

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