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 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 the sample mean () and sample coefficient of variation () the parameters and can be estimated:

: 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 the right conditions, timbers may survive over long periods of time and a recovered postpipe can simply be of solid wood.

Given their original purpose, military marching bands typically march in a forward direction with ( no variation of ) straight lines.

Given two variables x and y, y is directly proportional to x ( x and y vary directly, or x and y are in direct variation ) if there is a non-zero constant k such that

All but one (" Force of Nature ", from Backspacer ) of McCready's sole compositions for Pearl Jam use alternate tunings, such as open G on " Faithfull " ( from Yield ), a variation of open D on " Given to Fly ", and a variation of open G on " Marker in the Sand " ( from Pearl Jam ).

Given a function f belonging to L ^< sup > 1 </ sup >( Ω ), the total variation of f in Ω is defined as

Given a differentiable function defined on a bounded open set, the total variation of has the following expression

Given the variation among individuals with BWS and the lack of a simple diagnostic test, identifying BWS can be difficult.

Jael says, “ Given a reasonable variation, we are the same racial type … what you see is essentially the same genotype, modified by age, by circumstances, by education, by, diet, by learning, by God knows what ”( 161 ).

* 1974 Southwest Toe of Southeast Ridge, variation to the South Ridge, ascent by Peter Reagan, Joe Davidson, Bob Fries, Jim Given, Mark Greenfield, Pippo Lionni, Eric Morgan and Frank Uher.

Given this fact, though, some meters are more common or popular ; but there is a wide variation of less frequent combinations, as well.

Given the definition of morpheme as " the smallest meaningful unit " Nanosyntax aims to account for idioms where it is often an entire syntactic tree which contributes " the smallest meaningful unit.

Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.

Given an embedding of a rooted tree in the plane, if one fixes a direction of children ( starting from root, then first child, second child, etc.

Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree.

Given that humanity cannot exist except within a covenantal relationship with God, and all covenants use symbols to give us " the attestation of his grace ", he gives the tree, " not because it could confer on man that life with which he had been previously endued, but in order that it might be a symbol and memorial of the life which he had received from God.

Given before her thirteenth birthday to a man who makes her a slave, she sheds her tears on the tree she planted, which bears the best fruit in the world.

The original problem was stated in the form that has become known as the Euclidean Steiner tree problem or geometric Steiner tree problem: Given N points in the plane, the goal is to connect them by lines of minimum total length in such a way that any two points may be interconnected by line segments either directly or via other points and line segments.

The realization problem for Euclidean minimum spanning trees is stated as follows: Given a tree T = ( V, E ), find a location D ( u ) for each vertex u ∈ V so that T is a minimum spanning tree of D ( u ): u ∈ V, or determine that no such locations exist.

Given a square of 2 < sup > 2k </ sup > cells, 2 < sup > k </ sup > on a side, at the kth level of the tree, the hash table stores the 2 < sup > k-1 </ sup >- by-2 < sup > k-1 </ sup > square of cells in the center, 2 < sup > k-2 </ sup > generations in the future.

Given the fact that the tree was actually taller than Calhoun ( itself a five and six story building in different places ), the tree posed a real danger to the college structure and Calhoun students.

Given the environmental impact of the brown tree snake, studies have attempted to provide a capturing methodology to alleviate the detrimental effects of the tree snake.

Given a list of n points, the following algorithm uses a median-finding sort to construct a balanced k-d tree containing those points.