In probability theory, the law of total variance[1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law,[2] states that if and are random variables on the same probability space, and the variance of is finite, then
In language perhaps better known to statisticians than to probability theorists, the two terms are the "unexplained" and the "explained" components of the variance respectively (cf. fraction of variance unexplained, explained variation). In actuarial science, specifically credibility theory, the first component is called the expected value of the process variance (EVPV) and the second is called the variance of the hypothetical means (VHM).[3] These two components are also the source of the term "Eve's law", from the initials EV VE for "expectation of variance" and "variance of expectation".
^Neil A. Weiss, A Course in Probability, Addison–Wesley, 2005, pages 385–386.
^ Joseph K. Blitzstein and Jessica Hwang: "Introduction to Probability"
^Mahler, Howard C.; Dean, Curtis Gary (2001). "Chapter 8: Credibility" (PDF). In Casualty Actuarial Society (ed.). Foundations of Casualty Actuarial Science (4th ed.). Casualty Actuarial Society. pp. 525–526. ISBN 978-0-96247-622-8. Retrieved June 25, 2015.
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the lawoftotalvariance or variance decomposition formula or conditional variance formulas or lawof iterated variances also known as Eve's law, states...
give to the related lawoftotal expectation. Lawoftotal expectation LawoftotalvarianceLawoftotal covariance Lawoftotal cumulance Marginal distribution...
} The nomenclature in this article's title parallels the phrase lawoftotalvariance. Some writers on probability call this the "conditional covariance...
fundamental theorem of poker for one practical application. Lawoftotal probability LawoftotalvarianceLawoftotal covariance Lawoftotal cumulance Product...
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation...
the lawoftotalvariance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
probability theory and statistics, a conditional variance is the varianceof a random variable given the value(s) of one or more other variables. Particularly...
(N){\big (}\operatorname {E} (X){\big )}^{2}} which follows from the lawoftotalvariance. If N {\displaystyle N} has a Poisson distribution, then E ( N...
of value below. There are also different adaptations or alterations of Allan variance, notably the modified Allan variance MAVAR or MVAR, the total variance...
(D)=\lambda t\operatorname {E} (D).} Making similar use of the lawoftotalvariance, the variance can be calculated as: var ( Y ( t ) ) = E ( var ...
distribution's first two moments are given by the lawoftotal expectation and the lawoftotalvariance: E H [ X ] = E G [ E F [ X | θ ] ] {\displaystyle...
value and the varianceof the compound distribution can be derived in a simple way from lawoftotal expectation and the lawoftotalvariance. Thus E (...
The lawoftotal expectation and the lawoftotalvariance generalize naturally to conditional cumulants. The case n = 3, expressed in the language of (central)...
uncorrelated random variables Conditional expectation: law oftotal expectation, lawoftotalvariance Fatou's lemma and the monotone and dominated convergence...
is the convolution of their probability measures. Lawoftotal expectation LawoftotalvarianceLawoftotal covariance Lawoftotal cumulance Taylor expansions...
= 1/2, and that all odd central moments of X are 0. The lawoftotalvariance can be used to find the variance var(X), as follows. For the above set C1...
}}_{m})^{2}}.} Next, we use the lawoftotal expectation to compute μ m {\displaystyle \mu _{m}} and the lawoftotalvariance to compute σ m 2 {\displaystyle...
The varianceof the average is therefore asymptotic to 1 / log n {\displaystyle 1/\log n} and goes to zero. There are also examples of the weak law applying...
Time Variance Authority (TVA) is a fictional organization appearing in American comic books published by Marvel Comics. It is depicted as a group of timeline...
not the case, however, with the totalvarianceof the mean: As the unknown variance increases, the totalvarianceof the mean will increase proportionately...
ofvariance unexplained (FVU), since the second term compares the unexplained variance (varianceof the model's errors) with the totalvariance (of the...
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![{\displaystyle \operatorname {Var} (Y)=\operatorname {E} [\operatorname {Var} (Y\mid X)]+\operatorname {Var} (\operatorname {E} [Y\mid X]).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49180fb21d4dd636d8828788d7ebf1e411240316)