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In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data). Computations for analysis of variance involve the partitioning of a sum of SDM.
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics , the conditional variance is also known as the scedastic function or skedastic function . [ 1 ]
The law of total variance is a fundamental result in probability theory that expresses the variance of a random variable Y in terms of its conditional variances and conditional means given another random variable X.
In probability theory, the Fourier transform of the probability distribution of a real-valued random variable is closely connected to the characteristic function of that variable, which is defined as the expected value of , as a function of the real variable (the frequency parameter of the Fourier transform).
Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth).
In 1933, Andrei Kolmogorov published in German, his book on the foundations of probability theory titled Grundbegriffe der Wahrscheinlichkeitsrechnung, [i] where Kolmogorov used measure theory to develop an axiomatic framework for probability theory. The publication of this book is now widely considered to be the birth of modern probability ...