Given a fixed budget, this can allow an increased sample size.

Given a ( random ) sample the relation between the observations Y < sub > i </ sub > and the independent variables X < sub > ij </ sub > is formulated as

Given the difficulty in specifying exact distributions of sample statistics, many methods have been developed for approximating these.

Given samples from a population, the equation for the sample skewness above is a biased estimator of the population skewness.

Given a sample of wood, the variation of the tree ring growths provides not only a match by year, it can also match location because the climate across a continent is not consistent.

Given a sample of DNA, the instrument determines the order of the four bases — adenine, guanine, cytosine, and thymine — composing pieces of the sample.

Given the observed percentage difference p − q ( 2 % or 0. 02 ) and the standard error of the difference calculated above (. 03 ), any statistical calculator may be used to calculate the probability that a sample from a normal distribution with mean 0. 02 and standard deviation 0. 03 is greater than 0.

Given any set of points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian.

Given a sufficiently large sample size, a statistical comparison will always show a significant difference unless the population effect size is exactly zero.

Given a sample, the expectation function is approximated by the sample average

Given a random sample ( X < sub > i </ sub >, Y < sub > i </ sub >), i = 1, ..., n, each pair ( X < sub > i </ sub >, Y < sub > i </ sub >) satisfies

Given a random sample from the population, we estimate the population parameters and obtain the sample linear regression model:

Given a sample consisting of n independent observations x < sub > 1 </ sub >,..., x < sub > n </ sub > of a p-dimensional random vector X ∈ R < sup > p × 1 </ sup > ( a p × 1 column-vector ), an unbiased estimator of the ( p × p ) covariance matrix

Given a sample of n independent observations x < sub > 1 </ sub >,..., x < sub > n </ sub > of a p-dimensional zero-mean Gaussian random variable X with covariance R, the maximum likelihood estimator of R is given by

Given the estimation of from, the error bars of can be estimated by the sample variance using the unbiased estimate of the variance:

Given a random sample of T observations from this process, the ordinary least squares estimator is

: Given that there are almost eight times as many data points in this sample as in the previous analysis by Burbidge & Napier ( 2001 ), we must conclude that the previous detection of a periodic signal arose from the combination of noise and the effects of the window function.

Given that v < sup > 2 </ sup > ignores direction, it is logical to assume that the formula can be extended to the entire sample, replacing m with the entire sample's mass, equal to the molar mass times the number of moles n yielding

Given the sample ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, …, x < sub > n </ sub >), it is natural to estimate the characteristic function as

Given a total sample size greater than 1.

Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given a set of points in Euclidean space, the first principal component corresponds to a line that passes through the multidimensional mean and minimizes the sum of squares of the distances of the points from the line.

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given a total interaction cross section σ ( typically measured in barns ), the mean free path of a prompt neutron is where n is the nuclear number density.

Given an assembly of elements, the number of which decreases ultimately to zero, the mean lifetime,, ( also called simply the lifetime ) is the expected value of the amount of time before an object is removed from the assembly.

Given the mean arrival and service rates, then actual rates vary around these average values randomly and hence have to be determined using a cumulative probability distribution function.

Fallacious evaluation: " Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies.

Given a mean AGB lifetime of one Myr and an outer velocity of, its maximum radius can be estimated to be roughly ( 30 light years ).

Given a uniform distribution of backoff times, the expected backoff time is the mean of the possibilities.

Given that the Kuzyk limit is based directly on quantum mechanics, a breaching of the limit would mean that there are problems with quantum theory.

Given the distribution of Anglicans, this has tended to mean African mission partners joining Crosslinks.

Given Astaire's obsessive rehearsal habits, this was no mean task.

Given the possibility of underlying dimensions emerging from the scale, it is then the case that the scale is no longer balanced, since all the items primarily capturing authoritarian aggression are pro-trait worded ( higher scores mean more authoritarianism ) and all the items primarily measuring conventionalism are con-trait worded ( higher scores mean less authoritarianism ).

Given the atypical Romanian university admission system ( usually another exam making up for the rest of the process ), these percentages mean even less.

Given a set of parameters θ and an input vector x, the mean of the predicted Poisson distribution, as stated above, is given by

# Given name: Lǐ Jìnhái ()

Given an algebra, a homomorphism h thus defines two algebras homomorphic to, the image h () and The two are isomorphic, a result known as the homomorphic image theorem.

** Given name: Ji ()

Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.

Given two column vectors, their dot product can also be obtained by multiplying the transpose of one vector with the other vector and extracting the unique coefficient of the resulting 1 × 1 matrix.

Given the coefficient sequence for some M < J and all the difference sequences, k = M ,..., J-1, one computes recursively

Given two objects, A and B, each with n binary attributes, the Jaccard coefficient is a useful measure of the overlap that A and B share with their attributes.