If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).

If the diad consists of two identically oriented units, the diad is called a meso diad reflecting similar features as a meso compound.

If the y < sub > i </ sub > are independent and identically distributed, but not necessarily normally distributed, then

If the restriction of Q to a subspace U of V is identically zero, U is totally singular.

If n 3, the trace-free Ricci tensor vanishes identically if and only if

If the functions f and g are analytic and f is not identically zero in a neighbourhood of c on the complex plane, then the limit of f ( z )< sup > g ( z )</ sup > will always be 1.

If not performed identically ( because at this point in time, the player is now the earlier second Guybrush ), the player is returned to the start of the swamp.

If L / K is inseparable, then the trace map is identically 0.

If ƒ vanishes identically on all vectors it is said to be totally degenerate.

If one put the disk into the drive upside-down, the game played identically to the first side, except that the game was displayed vertically flipped.

* If f ( x ) is a polynomial, not identically zero, then it has an inverse g that is a distribution ; in other words, fg = 1 as distributions.

If each vocabulary is given a namespace, the ambiguity between identically named elements or attributes can be resolved.

If f is identically zero, then the theorem is trivially true.

If f is not identically zero, then A > 0.

* If the current density is identically zero, then the magnetic field is potential, i. e. the gradient of a scalar magnetic potential.

If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable

If the liquid and vapor are not evenly distributed across the superficial tower area as it enters the packed bed, the liquid to vapor ratio will not be correct in the packed bed and the required separation will not be achieved.

If all layers of an image change regularly but a large number of layer still need to be composited ( such as in distributed rendering ), the commutativity of a compositing operator can still be exploited to speed up computation through parallelism even when there is no gain from pre-computation.

If the legions were, indeed, broken up and distributed around all these small bases, then it implies a tactical use of the legions that has not previously been considered.

If the confinement is due many distributed Fresnel reflections, the device is termed a photonic crystal.

. If the gamodeme is very large ( theoretically, approaching infinity ), and all gene alleles are uniformly distributed by the gametes within it, the gamodeme is said to be panmictic.

If there was a net gain, one could in theory use a number of control nodes for which many hosts on the Internet form a distributed computing network completely unawares.

If the property is someday sold or subdivided, the proceeds must be distributed equally with no credits given for any excess than any one co-owner may have contributed to purchase the property.

If the seller is a competitive firm, the tax burden is distributed over the factors of production depending on the elasticities thereof ; this includes workers ( in the form of lower wages ), capital investors ( in the form of loss to shareholders ), landowners ( in the form of lower rents ), entrepreneurs ( in the form of lower wages of superintendence ) and customers ( in the form of higher prices ).

If several spatially distributed charges generate such an electric potential, e. g. in a solid, an electric field gradient may also be defined.

If this is compiled and distributed as part of a toolbox, a C # programmer, wishing to define a variable of type “” would encounter a problem: is a reserved word in C #.

If X and Y are normally distributed and independent, this implies they are " jointly normally distributed ", i. e., the pair ( X, Y ) must have multivariate normal distribution.

If the configuration is distributed according to at some moment of time, this holds for all times.

If the mass is evenly distributed, then the centre of mass of each limb is at its midpoint, and the limb has a moment of inertia of about that point.

If the work is to be distributed electronically, the final files are saved as formats appropriate to the target operating systems of the hardware used for reading.

If there is no dominant component to the scatter, then such a process will have zero mean and phase evenly distributed between 0 and 2π radians.

If one is dealing with continuous data, a typical assumption is that the continuous values associated with each class are distributed according to a Gaussian distribution.

If a virus is detected, the window turns red and the scan is stopped, and the alert is shown once you exit the screensaver ) or a distributed computing application ( such as the SETI @ home project ).

If the number of state variables necessary to describe future output is finite, the system is lumped ; if it is infinite, the system is distributed.

If X is a random variable with a normal distribution, then Y = exp ( X ) has a log-normal distribution ; likewise, if Y is log-normally distributed, then X = log ( Y ) has a normal distribution.

If log < sub > a </ sub >( Y ) is normally distributed, then so is log < sub > b </ sub >( Y ), for any two positive numbers a, b ≠ 1.

If, in preparing that shot for the inevitable showing to your friends, you interrupt the sequence to paste in a few frames of the child's grandmother watching this event, you have begun to be an artist in film ; ;

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If the mutated sequence is present in the patient's genome, the probe will bind to it and flag the mutation.

If the convention B < sub > 1 </ sub >=− is used, this sequence is also known as the first Bernoulli numbers ( / in OEIS ); with the convention B < sub > 1 </ sub >=+ is known as the second Bernoulli numbers ( / in OEIS ).

If a cabal can be implicated in a sequence of events, there is always the hope, however tenuous, of being able to break the cabal's power – or joining it and exercising some of that power oneself.

* If is the norm ( usually noted as ) defined in the square-summable sequence space ℓ < sup > 2 </ sup > ( which also matches the usual distance in a continuous and isotropic cartesian space ), then

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

This is a Cauchy sequence of rational numbers, but it does not converge towards any rational limit: If the sequence did have a limit x, then necessarily x < sup > 2 </ sup > = 2, yet no rational number has this property.

If the expression that defines the DFT is evaluated for all integers k instead of just for, then the resulting infinite sequence is a periodic extension of the DFT, periodic with period N.

If so, it is unclear how much Tatian may have borrowed from this previous author in determining his own narrative sequence of Gospel elements.

If shots are taken out of sequence, as is often the case, he will be alert to make sure that that beer glass is in the appropriate state.

) If a set is finite, its elements may be written as a sequence:

If the DNA sequence at a particular locus varies between individuals, the different forms of this sequence are called alleles.

If an equation can be put into the form f ( x ) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x < sub > 1 </ sub > in the basin of attraction of x, and let x < sub > n + 1 </ sub > = f ( x < sub > n </ sub >) for n ≥ 1, and the sequence

If there were a single intron within this sequence, it would look something like this:

A measure μ is countably subadditive: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … is a countable sequence of sets in Σ, not necessarily disjoint, then

If there are four alternative symbols ( corresponding to a musical instrument that can generate four different tones, one at a time ), the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11.

If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted.

* « If the same plain text sequence is given to disparate rendering processes, there is no expectation that rendered text in each instance should have the same appearance.

If 10 of those mutants are viable genotypes that may reproduce ( and some of whose offspring or grandchilden may mutate back into AGGT again ), we would consider that sequence a well-connected node in the cloud.

If instead only two of those mutants are viable, the rest being lethal mutations, then that sequence is poorly connected and most of its descendants will not reproduce.

If the mutation rate is zero, there is no exchange by mutation, and each sequence is its own species.

If W is irreducible then each type can, through a sequence of mutations ( i. e. powers of W ) mutate into all the other types.