A multivariate random variable or random vector is a vector X = (X_{1}, ..., X_{n}) whose components are scalarvalued random variables on the same probability space (Ω, P). Every such random vector gives rise to a probability measure on R^{n} with the Borel algebra as underlying sigmaalgebra. This measure is also known as the joint distribution of the random vector. The distributions of each of the component random variables X_{i} are called marginal distributions. In mathematics, a vector space (or linear space) is a collection of objects (known as vectors) which may be scaled and added; all linear combinations of vectors are themselves vectors. ...
In mathematics, scalars are components of vector spaces (and modules), usually real numbers, which can be multiplied into vectors by scalar multiplication. ...
A random variable is a mathematical function that maps outcomes of random experiments to numbers. ...
In mathematics, a probability space or probability measure is a set S, together with a Ïƒalgebra X on S and a measure P on that Ïƒalgebra such that P(S) = 1. ...
In mathematics, the Borel algebra (or Borel Ïƒalgebra) on a topological space X is a Ïƒalgebra of subsets of X associated to the topology of X. In the mathematics literature, there are at least two inequivalent definitions of this Ïƒalgebra: The minimal Ïƒalgebra containing the open sets. ...
In mathematics, a σalgebra (or σfield) X over a set S is a family of subsets of S which is closed under countable set operations; σalgebras are mainly used in order to define measures on S. The concept is important in mathematical analysis and probability theory. ...
