Algebra of random variables

Algebra of random variables

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. (Wikipedia).

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#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten

From playlist Linear Algebra

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From playlist Probability Theory

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From playlist Algebra

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From playlist Linear Algebra

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From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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From playlist Probability Theory

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From playlist Linear Algebra Lectures

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors

From playlist Linear Algebra

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Camille Male - Distributional symmetry of random matrices...

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From playlist Spectral properties of large random objects - Summer school 2017

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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From playlist Probability Theory

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Probability Theory - Part 10 - Random Variables [dark version]

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From playlist Probability Theory [dark version]

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Random Matrices and Their Limits - R. Speicher - Workshop 2 - CEB T3 2017

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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

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From playlist Geometry

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From playlist Noncommutative geometry meets topological recursion 2021

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From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021

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From playlist Linear Algebra

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