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The algebra of random variables in statistics, provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. Its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as well as dealing with operations such as finding the probability distributions and the expectations (or expected values), variances and covariances of such combinations.
In principle, the elementary algebra of random variables is equivalent to that of conventional non-random (or deterministic) variables. However, the changes occurring on the probability distribution of a random variable obtained after performing algebraic operations are not straightforward. Therefore, the behavior of the different operators of the probability distribution, such as expected values, variances, covariances, and moments, may be different from that observed for the random variable using symbolic algebra. It is possible to identify some key rules for each of those operators, resulting in different types of algebra for random variables, apart from the elementary symbolic algebra: Expectation algebra, Variance algebra, Covariance algebra, Moment algebra, etc.
and 28 Related for: Algebra of random variables information
and statistics, a multivariate randomvariable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because...
from 1979 The AlgebraofRandomVariables. If X {\displaystyle X} and Y {\displaystyle Y} are two independent, continuous randomvariables, described by...
complex randomvariables are a generalization of real-valued randomvariables to complex numbers, i.e. the possible values a complex randomvariable may take...
of the sum of normally distributed randomvariables is an instance of the arithmetic ofrandomvariables. This is not to be confused with the sum of normal...
mathematical physics, a random matrix is a matrix-valued randomvariable—that is, a matrix in which some or all of its entries are sampled randomly from a probability...
probability theory and statistics is a measure of the joint variability of two randomvariables. The sign of the covariance, therefore, shows the tendency...
there are alternative approaches for axiomatization, such as the algebraofrandomvariables. A probability space is a mathematical triplet ( Ω , F , P )...
the algebraofrandomvariables, inverse distributions are special cases of the class of ratio distributions, in which the numerator randomvariable has...
has been suggested as a "work-around". The ratio is one type ofalgebra for randomvariables: Related to the ratio distribution are the product distribution...
moments of a function f of a randomvariable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite...
of uncertainty (or propagation of error) is the effect ofvariables' uncertainties (or errors, more specifically random errors) on the uncertainty of...
statistics, a complex random vector is typically a tuple of complex-valued randomvariables, and generally is a randomvariable taking values in a vector...
σ-algebras G 1 ⊆ G 2 ⊆ F {\displaystyle {\mathcal {G}}_{1}\subseteq {\mathcal {G}}_{2}\subseteq {\mathcal {F}}} are defined. For a randomvariable X {\displaystyle...
{\displaystyle X} and Y {\displaystyle Y} are randomvariables on the same probability space, and the variance of Y {\displaystyle Y} is finite, then Var ...
book Algebraofrandomvariables Belief propagation Transferable belief model Dempster–Shafer theory Possibility theory Discrete randomvariable Probability...
conditional mean of a randomvariable is its expected value evaluated with respect to the conditional probability distribution. If the randomvariable can take...
probability theory and statistics, coskewness is a measure of how much three randomvariables change together. Coskewness is the third standardized cross...
joint cumulant of n randomvariables X1, ..., Xn, and the sum is over all partitions π {\displaystyle \pi } of the set { 1, ..., n } of indices, and "B...
the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are randomvariables on the...
occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions...
(/stəˈkæstɪk/) or random process is a mathematical object usually defined as a sequence ofrandomvariables in a probability space, where the index of the sequence...
convenient to express the theory using the algebraofrandomvariables: thus if X is used to denote a randomvariable corresponding to the observed data, the...
Aggregate data Aggregate pattern Akaike information criterion AlgebraofrandomvariablesAlgebraic statistics Algorithmic inference Algorithms for calculating...
definitions of multivariate normal distributions and linear algebra. Example Let X = [X1, X2, X3] be multivariate normal randomvariables with mean vector...
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