When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U / V has the standard Cauchy distribution.

When either type of noise is present, it is better to go with a higher bias, lower variance estimator.

When contains many candidate functions or the training set is not sufficiently large, empirical risk minimization leads to high variance and poor generalization.

When, this gives empirical risk minimization with low bias and high variance.

When is large, the learning algorithm will have high bias and low variance.

When a weighted mean is used, the variance of the weighted sample is different from the variance of the unweighted sample.

When received, the codeword vector variance is now, and its mean is the codeword sent.

When assessed upon a chi-square distribution, nonsignificant chi-square values indicate very little unexplained variance and thus, good model fit.

When the kickoff style is open to variance after each score, the desired rules are called out and whichever is heard first, is the accepted rule.

When used in this way, the proxy record ( tree ring width, say ) only reconstructs a certain amount of the variance of the original record.

When the mean is not known, the minimum mean squared error estimate of the variance of a sample from Gaussian distribution is achieved by dividing by n + 1, rather than n − 1 or n + 2.

When f is a set of non-linear combination of the variables x, it must usually be linearized by approximation to a first-order Taylor series expansion, though in some cases, exact formulas can be derived that do not depend on the expansion as is the case for the exact variance of products.

When normalized by dividing by the variance σ < sup > 2 </ sup >, the autocovariance C becomes the autocorrelation coefficient function c,

When effect of variance is concerned, there are two types of variances:

* When actual results are better than expected results given variance is described as favorable variance.

* When actual results are worse than expected results given variance is described as adverse variance, or unfavourable variance.

Until October 2010, After United States v. Pepper ( 2010 ), " When a defendant ’ s sentence has been set aside on appeal, a district court at resentencing may consider evidence of the defendant ’ s postsentencing rehabilitation, and such evidence may, in appropriate cases, support a downward variance from the now-advisory Guidelines range.

When referring to bone or cartilage, mesenchymal stem cell ( mesoderm origin ) are undifferentiated meaning they can differentiate into different variance of generative cells ( MSC ) are commonly known as osteochondrogenic ( or osteogenic, chondrogenic, osteoprogenitor, etc.

When estimating the population mean using an independent and identically distributed ( iid ) sample of size n, where each data value has variance σ < sup > 2 </ sup >, the standard error of the sample mean is:

When the noise is additive, i. e. it is added to the signal ( rather than multiplied for example ) and the statistics of the noise process are known to follow the gaussian statistical law, then a linear filter is known to be optimal under a number of possible criteria ( for example the mean square error criterion, aiming at minimizing the variance of the error ).

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

When a specific allophone ( from a set of allophones that correspond to a phoneme ) must be selected in a given context ( i. e. using a different allophone for a phoneme will cause confusion or make the speaker sound non-native ), the allophones are said to be complementary ( i. e. the allophones complement each other, and one is not used in a situation where the usage of another is standard ).

When non-native speakers speak Hindi-Urdu, they might pronounce / व / in ' व ् रत ' as, i. e. as wrat instead of the correct vrat.

When they are realized without much allophonic variation, a simple ( i. e. ' broad ') transcription is used.

When shuffled, the second deck is placed to the shuffler's right, i. e. to the next dealer's left.

When Croatia declared independence in 1991, the only true motorways in the country were Zagreb – Karlovac ( the northernmost part of A1 ) and Zagreb-Slavonski Brod ( A3 ), the latter being part of the highway " Bratstvo i jedinstvo ".

When the radiometer is heated in the absence of a light source, it turns in the forward direction ( i. e. black sides trailing ).

When scientists want to express a specific protein in a cell that does not normally express that protein ( i. e., heterologous expression ), they will transfer the cDNA that codes for the protein to the recipient cell.

When, in the 1970s and 1980s, Jürgen Habermas redefined critical social theory as a theory of communication, i. e. communicative competence and communicative rationality on the one hand, distorted communication on the other, the two versions of critical theory began to overlap or intertwine to a much greater degree than before.

When this state is needed, i. e., when it is decided by a database administrator to bring the database back to this state ( e. g., by specifying this state by a desired point in time when the database was in this state ), these files are utilized to restore that state.

When the two waves are in phase, i. e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i. e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero.

When in doubt ( i. e. if a different name has not been clearly set in the literature ), the hierarchy expressed by the nomenclature should correspond to dynamically distinct ( sub -) systems in order of their dynamical relevance.

When moving from a denser medium into a less dense one ( i. e., n < sub > 1 </ sub > > n < sub > 2 </ sub >), above an incidence angle known as the critical angle, all light is reflected and R < sub > s </ sub > = R < sub > p </ sub > = 1.

When describing graviton interactions, the classical theory ( i. e., the tree diagrams ) and semiclassical corrections ( one-loop diagrams ) behave normally, but Feynman diagrams with two ( or more ) loops lead to ultraviolet divergences ; that is, infinite results that cannot be removed because the quantized general relativity is not renormalizable, unlike quantum electrodynamics.

When referring to RAM sizes it most often ( see binary prefix adoption ) has a binary interpretation of 1024 < sup > 3 </ sup > bytes, i. e. as an alias for gibibyte.

When he died as king of the combined kingdom in 900, Domnall II ( Donald II ) was the first man to be called rí Alban ( i. e. King of Alba ).

When storing records in a large unsorted file, one may use a hash function to map each record to an index into a table T, and collect in each bucket T a list of the numbers of all records with the same hash value i. Once the table is complete, any two duplicate records will end up in the same bucket.

When dissolving a lipophilic or amphiphilic substance in a polar environment, the polar molecules ( i. e., water in an aqueous solution ) become more ordered around the dissolved lipophilic substance, since the polar molecules cannot form hydrogen bonds to the lipophilic areas of the amphiphile.

When linguists study the lexicon, they consider such things as what constitutes a word ; the word-concept relationship ; lexical access and lexical access failure ; how a word's phonology, syntax, and meaning intersect ; the morphology-word relationship ; vocabulary structure within a given language ; language use ( that is, pragmatics ); language acquisition ; the history and evolution of words ( i. e. etymology ); and the relationships between words, often studied within philosophy of language.

If E < sub > i </ sub > is applied to the inverting input, the circuit is an inverting positive-level detector: When E < sub > i </ sub > is above V < sub > ref </ sub >, V < sub > O </ sub > equals − V < sub > sat </ sub >.

When the privilege is abused by a player ( i. e. the player does not suspect cheating, but asks to see the cards just to get insight on another player's style or betting patterns ), he may be warned by the dealer, or even removed from the table.

When the dealer is not a player ( i. e. a casino employee ), the cut is mandatory and is usually performed by the dealer.