Editing Algebra of random variables (section)

{{Short description|Mathematical technique}}

{{More footnotes|date=November 2010}}

In [[statistics]], the '''algebra of random variables''' provides rules for the [[Symbolic computation|symbolic manipulation]] of [[random variable]]s, 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 distribution]]s and the [[expected values|expectations]] (or expected values), [[variance]]s and [[covariance]]s 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 operation]]s are not straightforward. Therefore, the behavior of the different operators of the probability distribution, such as expected values, variances, covariances, and [[Moment (mathematics)|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.