Information about Multivariate Random Variable
A multivariate random variable or random vector is a vector X = (X1, ..., Xn) whose components are scalar-valued random variables on the same probability space (Ω, P). Every such random vector gives rise to a probability measure on Rn with the Borel algebra as underlying sigma-algebra. This measure is also known as the joint distribution of the random vector. The distributions of each of the component random variables Xi are called marginal distributions.
In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. More formally, a vector space is a set on which two operations, called (vector) addition and (scalar) multiplication, are
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scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.
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A random variable is an abstraction of the intuitive concept of chance into the theoretical domains of mathematics, forming the foundations of probability theory and mathematical statistics.
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In probability theory, the definition of the probability space is the foundation of probability theory. It was introduced by Kolmogorov in the 1930s. For an algebraic alternative to Kolmogorov's approach, see algebra of random variables.
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In mathematics, the Borel algebra (or Borel σ-algebra) on a topological space X is a σ-algebra of subsets of X associated with the topology of X.
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In mathematics, a σ-algebra (or sigma-algebra) over a set X is a nonempty collection Σ of subsets of X that is closed under complementation and countable unions of its members.
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joint distribution of X and Y is the distribution of X and Y together.
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The discrete case
For discrete random variables, the joint probability mass function can be written as Pr(X = x & Y..... Click the link for more information.
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