Misplaced Pages

#405594

41-485: [REDACTED] Look up variant  or variants in Wiktionary, the free dictionary. Variant may refer to: Arts and entertainment [ edit ] Variant (magazine) , a former British cultural magazine Variant cover , an issue of comic books with varying cover art Variant (novel) , a novel by Robison Wells " The Variant ", 2021 episode of

82-481: A x 2 + b {\displaystyle \varphi (x)=ax^{2}+b} , where a > 0 . This also holds in the multidimensional case. Unlike the expected absolute deviation , the variance of a variable has units that are the square of the units of the variable itself. For example, a variable measured in meters will have a variance measured in meters squared. For this reason, describing data sets via their standard deviation or root mean square deviation

123-579: A Theme (disambiguation) Rate of change (disambiguation) Repetition (disambiguation) Variability (disambiguation) Variance Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Variant . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Variant&oldid=1182415626 " Category : Disambiguation pages Hidden categories: Short description

164-579: A Theme (disambiguation) Rate of change (disambiguation) Repetition (disambiguation) Variability (disambiguation) Variance Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Variant . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Variant&oldid=1182415626 " Category : Disambiguation pages Hidden categories: Short description

205-489: A constant, the variance is scaled by the square of that constant: The variance of a sum of two random variables is given by where Cov ⁡ ( X , Y ) {\displaystyle \operatorname {Cov} (X,Y)} is the covariance . In general, for the sum of N {\displaystyle N} random variables { X 1 , … , X N } {\displaystyle \{X_{1},\dots ,X_{N}\}} ,

246-447: A continuous function φ {\displaystyle \varphi } satisfies a r g m i n m E ( φ ( X − m ) ) = E ( X ) {\displaystyle \mathrm {argmin} _{m}\,\mathrm {E} (\varphi (X-m))=\mathrm {E} (X)} for all random variables X , then it is necessarily of the form φ ( x ) =

287-472: A generator of hypothetical observations. If an infinite number of observations are generated using a distribution, then the sample variance calculated from that infinite set will match the value calculated using the distribution's equation for variance. Variance has a central role in statistics, where some ideas that use it include descriptive statistics , statistical inference , hypothesis testing , goodness of fit , and Monte Carlo sampling . The variance of

328-718: A novel by Robison Wells " The Variant ", 2021 episode of the TV series Loki Sylvie (Marvel Cinematic Universe) , a character who was originally referred to as the Variant "Variant", a fictional term in the Marvel Cinematic Universe pertaining to the multiverse Gaming [ edit ] Chess variant , a game derived from, related to or similar to chess in at least one respect List of poker variants List of Tetris variants Mathematics and computing [ edit ] Variant (logic) ,

369-470: A random variable X {\displaystyle X} is the expected value of the squared deviation from the mean of X {\displaystyle X} , μ = E ⁡ [ X ] {\displaystyle \mu =\operatorname {E} [X]} : This definition encompasses random variables that are generated by processes that are discrete , continuous , neither , or mixed. The variance can also be thought of as

410-473: A set of n {\displaystyle n} equally likely values can be equivalently expressed, without directly referring to the mean, in terms of squared deviations of all pairwise squared distances of points from each other: If the random variable X {\displaystyle X} has a probability density function f ( x ) {\displaystyle f(x)} , and F ( x ) {\displaystyle F(x)}

451-429: A subset is available, and the variance calculated from this is called the sample variance. The variance calculated from a sample is considered an estimate of the full population variance. There are multiple ways to calculate an estimate of the population variance, as discussed in the section below. The two kinds of variance are closely related. To see how, consider that a theoretical probability distribution can be used as

SECTION 10

#1732776820406

492-482: A term or formula obtained from another one by consistently renaming all variables Variant symlinks , a symbolic link to a file that has a variable name embedded in it Variant type , in programming languages Z-variant , unicode characters that share the same etymology but have slightly different appearances Computer security [ edit ] In network security, varieties of computer worms are called variants. Biology [ edit ] Allele ,

533-482: A term or formula obtained from another one by consistently renaming all variables Variant symlinks , a symbolic link to a file that has a variable name embedded in it Variant type , in programming languages Z-variant , unicode characters that share the same etymology but have slightly different appearances Computer security [ edit ] In network security, varieties of computer worms are called variants. Biology [ edit ] Allele ,

574-407: A variant of a gene In microbiology and virology, a variant , or 'genetic variant' is a subtype of a known microorganism. Vehicles [ edit ] Volkswagen Variant , an air-cooled station wagon produced until the early 1980s TeST TST-5 Variant , a Czech aircraft design of the 1990s Other uses [ edit ] Variant name (geography) , a name for a geographic feature that

615-407: A variant of a gene In microbiology and virology, a variant , or 'genetic variant' is a subtype of a known microorganism. Vehicles [ edit ] Volkswagen Variant , an air-cooled station wagon produced until the early 1980s TeST TST-5 Variant , a Czech aircraft design of the 1990s Other uses [ edit ] Variant name (geography) , a name for a geographic feature that

656-416: Is a discrete random variable assuming possible values y 1 , y 2 , y 3 … {\displaystyle y_{1},y_{2},y_{3}\ldots } with corresponding probabilities p 1 , p 2 , p 3 … , {\displaystyle p_{1},p_{2},p_{3}\ldots ,} , then in the formula for total variance,

697-483: Is different from Wikidata All article disambiguation pages All disambiguation pages variant [REDACTED] Look up variant  or variants in Wiktionary, the free dictionary. Variant may refer to: Arts and entertainment [ edit ] Variant (magazine) , a former British cultural magazine Variant cover , an issue of comic books with varying cover art Variant (novel) ,

738-426: Is different from Wikidata All article disambiguation pages All disambiguation pages Variance An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation ; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of

779-552: Is given by on the interval [0, ∞) . Its mean can be shown to be Using integration by parts and making use of the expected value already calculated, we have: Thus, the variance of X is given by A fair six-sided die can be modeled as a discrete random variable, X , with outcomes 1 through 6, each with equal probability 1/6. The expected value of X is ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 7 / 2. {\displaystyle (1+2+3+4+5+6)/6=7/2.} Therefore,

820-481: Is not in primary use Variant Chinese character , Chinese characters that can be used interchangeably Orthographical variant , a variant spelling of a botanical name Varyant , a road in İzmir, Turkey In an invitation to tender , a supplier response which in part offers a solution different from that specified by the buyer See also [ edit ] Variety (disambiguation) Variation (disambiguation) Change (disambiguation) Variations on

861-481: Is not in primary use Variant Chinese character , Chinese characters that can be used interchangeably Orthographical variant , a variant spelling of a botanical name Varyant , a road in İzmir, Turkey In an invitation to tender , a supplier response which in part offers a solution different from that specified by the buyer See also [ edit ] Variety (disambiguation) Variation (disambiguation) Change (disambiguation) Variations on

SECTION 20

#1732776820406

902-478: Is often preferred over using the variance. In the dice example the standard deviation is √ 2.9 ≈ 1.7 , slightly larger than the expected absolute deviation of 1.5. The standard deviation and the expected absolute deviation can both be used as an indicator of the "spread" of a distribution. The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance ,

943-406: Is part of a theoretical probability distribution and is defined by an equation. The other variance is a characteristic of a set of observations. When variance is calculated from observations, those observations are typically measured from a real-world system. If all possible observations of the system are present, then the calculated variance is called the population variance. Normally, however, only

984-472: Is the corresponding cumulative distribution function , then or equivalently, where μ {\displaystyle \mu } is the expected value of X {\displaystyle X} given by In these formulas, the integrals with respect to d x {\displaystyle dx} and d F ( x ) {\displaystyle dF(x)} are Lebesgue and Lebesgue–Stieltjes integrals, respectively. If

1025-403: Is the expected value. That is, (When such a discrete weighted variance is specified by weights whose sum is not 1, then one divides by the sum of the weights.) The variance of a collection of n {\displaystyle n} equally likely values can be written as where μ {\displaystyle \mu } is the average value. That is, The variance of

1066-426: Is used frequently in theoretical statistics; however the expected absolute deviation tends to be more robust as it is less sensitive to outliers arising from measurement anomalies or an unduly heavy-tailed distribution . Variance is invariant with respect to changes in a location parameter . That is, if a constant is added to all values of the variable, the variance is unchanged: If all values are scaled by

1107-419: The conditional variance Var ⁡ ( X ∣ Y ) {\displaystyle \operatorname {Var} (X\mid Y)} may be understood as follows. Given any particular value y of the random variable  Y , there is a conditional expectation E ⁡ ( X ∣ Y = y ) {\displaystyle \operatorname {E} (X\mid Y=y)} given

1148-750: The covariance of a random variable with itself: The variance is also equivalent to the second cumulant of a probability distribution that generates X {\displaystyle X} . The variance is typically designated as Var ⁡ ( X ) {\displaystyle \operatorname {Var} (X)} , or sometimes as V ( X ) {\displaystyle V(X)} or V ( X ) {\displaystyle \mathbb {V} (X)} , or symbolically as σ X 2 {\displaystyle \sigma _{X}^{2}} or simply σ 2 {\displaystyle \sigma ^{2}} (pronounced " sigma squared"). The expression for

1189-491: The law of total variance is: If X {\displaystyle X} and Y {\displaystyle Y} are two random variables, and the variance of X {\displaystyle X} exists, then The conditional expectation E ⁡ ( X ∣ Y ) {\displaystyle \operatorname {E} (X\mid Y)} of X {\displaystyle X} given Y {\displaystyle Y} , and

1230-475: The TV series Loki Sylvie (Marvel Cinematic Universe) , a character who was originally referred to as the Variant "Variant", a fictional term in the Marvel Cinematic Universe pertaining to the multiverse Gaming [ edit ] Chess variant , a game derived from, related to or similar to chess in at least one respect List of poker variants List of Tetris variants Mathematics and computing [ edit ] Variant (logic) ,

1271-568: The event  Y  =  y . This quantity depends on the particular value  y ; it is a function g ( y ) = E ⁡ ( X ∣ Y = y ) {\displaystyle g(y)=\operatorname {E} (X\mid Y=y)} . That same function evaluated at the random variable Y is the conditional expectation E ⁡ ( X ∣ Y ) = g ( Y ) . {\displaystyle \operatorname {E} (X\mid Y)=g(Y).} In particular, if Y {\displaystyle Y}

Variant - Misplaced Pages Continue

1312-679: The first term on the right-hand side becomes where σ i 2 = Var ⁡ [ X ∣ Y = y i ] {\displaystyle \sigma _{i}^{2}=\operatorname {Var} [X\mid Y=y_{i}]} . Similarly, the second term on the right-hand side becomes where μ i = E ⁡ [ X ∣ Y = y i ] {\displaystyle \mu _{i}=\operatorname {E} [X\mid Y=y_{i}]} and μ = ∑ i p i μ i {\displaystyle \mu =\sum _{i}p_{i}\mu _{i}} . Thus

1353-449: The function x 2 f ( x ) {\displaystyle x^{2}f(x)} is Riemann-integrable on every finite interval [ a , b ] ⊂ R , {\displaystyle [a,b]\subset \mathbb {R} ,} then where the integral is an improper Riemann integral . The exponential distribution with parameter λ is a continuous distribution whose probability density function

1394-467: The generator of random variable X {\displaystyle X} is discrete with probability mass function x 1 ↦ p 1 , x 2 ↦ p 2 , … , x n ↦ p n {\displaystyle x_{1}\mapsto p_{1},x_{2}\mapsto p_{2},\ldots ,x_{n}\mapsto p_{n}} , then where μ {\displaystyle \mu }

1435-424: The predicted score and the error score, where the latter two are uncorrelated. Similar decompositions are possible for the sum of squared deviations (sum of squares, S S {\displaystyle {\mathit {SS}}} ): The population variance for a non-negative random variable can be expressed in terms of the cumulative distribution function F using This expression can be used to calculate

1476-568: The same value: If a distribution does not have a finite expected value, as is the case for the Cauchy distribution , then the variance cannot be finite either. However, some distributions may not have a finite variance, despite their expected value being finite. An example is a Pareto distribution whose index k {\displaystyle k} satisfies 1 < k ≤ 2. {\displaystyle 1<k\leq 2.} The general formula for variance decomposition or

1517-512: The total variance is given by A similar formula is applied in analysis of variance , where the corresponding formula is here M S {\displaystyle {\mathit {MS}}} refers to the Mean of the Squares. In linear regression analysis the corresponding formula is This can also be derived from the additivity of variances, since the total (observed) score is the sum of

1558-450: The variance can be expanded as follows: In other words, the variance of X is equal to the mean of the square of X minus the square of the mean of X . This equation should not be used for computations using floating point arithmetic , because it suffers from catastrophic cancellation if the two components of the equation are similar in magnitude. For other numerically stable alternatives, see algorithms for calculating variance . If

1599-417: The variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard deviation is more commonly reported as a measure of dispersion once the calculation is finished. Another disadvantage is that the variance is not finite for many distributions. There are two distinct concepts that are both called "variance". One, as discussed above,

1640-585: The variance in situations where the CDF, but not the density , can be conveniently expressed. The second moment of a random variable attains the minimum value when taken around the first moment (i.e., mean) of the random variable, i.e. a r g m i n m E ( ( X − m ) 2 ) = E ( X ) {\displaystyle \mathrm {argmin} _{m}\,\mathrm {E} \left(\left(X-m\right)^{2}\right)=\mathrm {E} (X)} . Conversely, if

1681-423: The variance of X is The general formula for the variance of the outcome, X , of an n -sided die is The following table lists the variance for some commonly used probability distributions. Variance is non-negative because the squares are positive or zero: The variance of a constant is zero. Conversely, if the variance of a random variable is 0, then it is almost surely a constant. That is, it always has

Variant - Misplaced Pages Continue

#405594