Thus the observed radiation density ( the sky brightness of extragalactic background light ) can be independent of finiteness of the Universe.

For n independent and identically distributed continuous random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution function G ( x ) and probability density function g ( x ) the range of the X < sub > i </ sub > is the range of a sample of size n from a population with distribution function G ( x ).

For n nonidentically distributed independent continuous random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution functions G < sub > 1 </ sub >( x ), G < sub > 2 </ sub >( x ), ..., G < sub > n </ sub >( x ) and probability density functions g < sub > 1 </ sub >( x ), g < sub > 2 </ sub >( x ), ..., g < sub > n </ sub >( x ), the range has cumulative distribution function

However, shot noise is temperature and frequency independent, in contrast to Johnson – Nyquist noise, proportional to temperature, and flicker noise, with the spectral density decreasing with the frequency.

The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions.

" Although independent companies typically serve these areas, RBOC LECs still have vast territories of low population density regions of the country.

This form of the ideal gas law is very useful because it links pressure, density, and temperature in a unique formula independent of the quantity of the considered gas.

* Naive Bayes classifier — assumes independent binomial conditional density models.

Suppose there is a sample of n independent and identically distributed observations, coming from a distribution with an unknown probability density function f < sub > 0 </ sub >(·).

It is a function of the square root of the absolute temperature, but is nearly independent of pressure or density for a given gas.

Although, in the case of gases only, the speed of sound may be expressed in terms of a ratio of both density and pressure, these quantities are not fully independent of each other, and canceling their common contributions from physical conditions leads to a velocity expression using the independent variables of temperature, composition, and heat capacity noted above.

He ascertained that water was denser about 40 ° F ( 4 ° C ) than at the temperature of freezing, expanding equally on each side of the maximum ; and he was the originator of the theory, later readvanced by John Dalton, that the quantity of water vapour contained in any space is independent of the presence or density of the air, or of any other elastic fluid.

Hebden Bridge has built a reputation for “ great little shops ” and has an unusually high density of independent shops for a UK town of its size.

Optimal use of dither ( triangular probability density function dither in PCM systems ) has the effect of making the rms quantization error independent of signal level ( Dunn 2003: 143 ), and allows signal information to be retained below the least significant bit of the digital system ( Stuart n. d .: 3 ).

The density for a liquid is almost independent of the liquid conditions ; however, this is not the case for gas, the density of which depends greatly upon pressure, temperature and to a lesser extent, the gas composition.

Unlike more specialised birds such as the Eurasian Nuthatch and the Eurasian Treecreeper, both of which forage on tree trunks, the kinglets do not need large woodlands, and their population density is independent of forest size.

Unlike more specialised birds such as Eurasian Nuthatch and Common Treecreeper, both of which forage on trunks, the crests do not need large woodlands, and their population density is independent of forest size.

The density of the sum of two independent real-valued random variables equals the convolution of the density functions of the original variables.

Thus, the density of the sum of m + n terms of a sequence of independent identically distributed variables equals the convolution of the densities of the sums of m terms and of n term.

Then the densities of the sums of two, three, and four independent identically distributed variables, each having the original density, are shown in the following figures.

The K factor, a term used to denote the rate of heat transmission through a material ( B.t.u./sq. ft. of material/hr./*0F./in. of thickness ) ranges from 0.24 to 0.28 for flexible urethane foams and from 0.12 to 0.16 for rigid urethane foams, depending upon the formulation, density, cell size, and nature of blowing agents used.

In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 10 < sup > 78 </ sup > in volume, driven by a negative-pressure vacuum energy density.

" Pressing times to the desired density could vary by factor of three depending on the atmospheric humidity.

* Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region.

Specifically, if the vacuum energy is negative and its absolute value is substantially larger than it appears to be in the observed universe ( say, a factor of 10 larger ), holding all other variables ( e. g. matter density ) constant, that would mean that the universe is closed ; furthermore, its lifetime would be shorter than the age of our universe, possibly too short for the intelligent life to form.

Specifically, when the scale of the universe doubles, the density of matter is reduced by a factor of 8, but the density of dark energy is nearly unchanged ( it is exactly constant if the dark energy is a cosmological constant ).

In 1965, Moore examined the density of transistors at which cost is minimized, and observed that, as transistors were made smaller through advances in photolithography, this number would increase at " a rate of roughly a factor of two per year ".

In facsimile systems, the cooperation factor is the product of the total image scanning length and the scanning density, given by CF = L σ, where L is the scanning line length and σ is the scanning line density, both in compatible units.

For example, a 20 cm line and a line density of 6 scanning pitches per centimeter would yield a cooperation factor of 120.

One confounding factor, which has been the subject of many studies, is residential self-selection: people who prefer to drive tend to move towards low density suburbs, whereas people who prefer to walk, cycle or use transit tend to move towards higher density urban areas, better served by public transport.

LDL particles vary in size and density, and studies have shown that a pattern that has more small dense LDL particles, called Pattern B, equates to a higher risk factor for coronary heart disease ( CHD ) than does a pattern with more of the larger and less dense LDL particles ( Pattern A ).

The normalization factor required for the density operator to have trace 1 is the quantum mechanical version of the partition function.

The acceleration of the ions also entails a decrease in the density, usually by a factor of about 2 depending on the details.

i. e. the density ƒ can be factored into a product such that one factor, h, does not depend on θ and the other factor, which does depend on θ, depends on x only through T ( x ).

High density composites are an economically viable option when certain materials are deemed hazardous and are banned ( such as lead ) or when secondary operations costs ( such as machining, finishing, or coating ) are a factor.

In addition, moment of inertia should not be confused with polar moment of inertia ( more specifically, polar moment of inertia of area ), which is a measure of an object's ability to resist torsion ( twisting ) only, although, mathematically, they are similar: if the solid for which the moment of inertia is being calculated has uniform thickness in the direction of the rotating axis, and also has uniform mass density, the difference between the two types of moments of inertia is a factor of mass per unit area.

Though they are more expensive, they do have a higher power density and with the appropriate drive electronics are actually better suited to the application, however price is always an important factor.

No other critical factors were affected, such as bone density, cholesterol levels, lipid measurements, maximal oxygen consumption, or any other factor that would indicate increased fitness.

The dependence of this upon geometry, mass, and density appears through the factor q.

In terms of the total mass M, the nuclear mass m, the density ρ, and a fudge factor f which takes into account geometrical and other effects, criticality corresponds to

The spectral density of the wave, when multiplied by an appropriate factor, will give the power carried by the wave, per unit frequency, known as the power spectral density ( PSD ) of the signal.