Real-valued functions encountered in applications tend to be measurable ; however, it is not difficult to find non-measurable functions.

Real-valued special uniformly continuous functions on the metric space can also be characterized as the set of all functions that are restrictions to of uniformly continuous functions over any normed space isometrically containing.

* H. V. Sorensen, D. L. Jones, M. T. Heideman, and C. S. Burrus, " Real-valued fast Fourier transform algorithms ," IEEE Trans.

Real-valued signals have Fourier spectra with symmetry about zero.

A binomial experiment can produce random variables other than the number of successes.

The several trials of a binomial experiment produce a new random variable X, the total number of successes, which is just the sum of the random variables associated with the single trials.

The number of successes on each shot is a value of a random variable that has values 0 or 1, and there are 5 such random variables here.

It was assumed that the sampling procedure was purely random with respect to the personality variables under investigation.

; Random effect: An effect associated with input variables chosen at random from a population having a large or infinite number of possible values.

Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments ( a multi-variable generalization of simple differences ) differ from the fixed-effects model.

In contrast, randomized algorithms like the PPSZ algorithm by Paturi, Pudlak, Saks, and Zani set variables in a random order according to some heuristics, for example bounded-width resolution.

Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

The simplest Cauchy distribution is called the standard Cauchy distribution is the distribution of a random variable that is the ratio of two independent standard normal random variables.

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.

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 ).

Firstly, in estimating the probability density functions of random variables and secondly in estimating the spectral density function of a time series.

It is often convenient to express the theory using the algebra of random variables: thus if X is used to denote a random variable corresponding to the observed data, the estimator ( itself treated as a random variable ) is symbolised as a function of that random variable,.

Commenting on this, other writers ( such as John von Neumann and David Bohm ) have suggested that consequently there would have to be ' hidden ' variables responsible for random measurement results, something which was not expressly claimed in the original paper.

Programming features such as randomization, variables, and intermap script activation enable smooth hub gameplay and are responsible for most of the special effects within the game: On-screen messages ; random sound effect and monster spawning ; sidedef texture changes ; versatile control of polyobjects ; level initialization for deathmatch ; and even complex environment changes such as earthquakes manipulating floor levels and textures.

The most important quantities of information are entropy, the information in a random variable, and mutual information, the amount of information in common between two random variables.

The joint entropy of two discrete random variables and is merely the entropy of their pairing:.

Shannon's entropy represents an absolute limit on the best possible lossless compression of any communication, under certain constraints: treating messages to be encoded as a sequence of independent and identically distributed random variables, Shannon's source coding theorem shows that, in the limit, the average length of the shortest possible representation to encode the messages in a given alphabet is their entropy divided by the logarithm of the number of symbols in the target alphabet.

One deck represents random Alpha Mutations, which can be drawn to gain temporary powers, and the other contains various Omega Tech, powerful technological devices that could possibly backfire on those that use them.

That is, the alleles in the offspring in the population are a random sample of those in the parents.

Both support random access, as well as head and tail operations similar to those available in Lisp.

This system is an example, and similar to those of dedicated hardware random number generators.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

A variant of the basic approach is to rely on the properties ( including whatever vulnerabilities might be present ) of a product which is not widely adopted, thus lowering the prominence of those vulnerabilities ( should they become known ) against random or even automated attacks.

According to Max Boot's book War Made New ( 2006, pg 122 ), sometime between 1803 and 1809, the Prussian General Staff developed war games, with staff officers moving metal pieces around on a game table ( with blue pieces representing their forces and red pieces those of the enemy ), using dice rolls to indicate random chance and with a referee scoring the results.

On the contrary, Harris suggests that either peer groups or random environmental factors ( i. e., those that are independent of family upbringing ) are more important than family environmental effects.

The random distribution of the orientation of the ellipsoids in a glass produces a macroscopically isotropic medium, but a strong pump laser induces an anisotropic distribution by selectively exciting those ions that are more aligned with the optical field vector of the pump.

Once the potentially useful microsatellites are determined ( removing non-useful ones such as those with random inserts within the repeat region ), the flanking sequences can be used to design oligonucleotide primers which will amplify the specific microsatellite repeat in a PCR reaction.

* The distances between where certain values occur are distributed differently from those in a random sequence distribution.

Fractals are sometimes combined with human-assisted evolutionary algorithms, either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and producing new variations, to avoid dealing cumbersome or unpredictable parameters, or collectively, like in the Electric Sheep project, where people use fractal flames rendered with distributed computing as their screensaver and " rate " the flame they are viewing, influencing the server, which reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.

The low-level interface to flash memory chips differs from those of other memory types such as DRAM, ROM, and EEPROM, which support bit-alterability ( both zero to one and one to zero ) and random access via externally accessible address buses.

The direct access capability, occasionally and incorrectly called random access ( although that term survives when referring to memory or RAM ), of those devices stood in contrast to sequential access used in tape drives.

This count includes relatives of the partisans, their supporters, Czech elites suspected of disloyalty and random victims like those from Lidice.

" The application " implements all the standards very well, and for those who prefer to keep desktop clutter to a minimum but still enjoy fighting with random strangers on IRC, ChatZilla is a must-have.

Because the Germans needed the Sonderkommandos to remain physically able, they were granted moderately less squalid living conditions than other inmates: they slept in their own barracks, which more than any other in the camp resembled normal human dwellings ; they were allowed to keep and use various goods such as food, medicines and cigarettes brought by those who were sent to the gas chambers ; and, unlike ordinary inmates, they were not subject to arbitrary, random killing by guards.

Another useful distinction is between traits that are likely to be adaptations ( such as the nose ) vs. those that are byproducts of adaptations ( such the white color of bones ), or are due to random variation ( non-adaptive variation in, say, nose shape or size ).

It is a small piece of code that does little other than generate random IP addresses and send itself out to those addresses.

The Kalman filter, also known as linear quadratic estimation ( LQE ), is an algorithm which uses a series of measurements observed over time, containing noise ( random variations ) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those that would be based on a single measurement alone.

While generic enemy units do appear in the game, most random battles are fought against one or more generals randomly selected from those roaming the lands the player's party is traveling through at the time.

When laying eggs in nests already parasitised, the female cuckoos removed one egg at random, showing no discrimination between the Great Reed Warbler eggs and those of other cuckoos.

The Chomskybot is a program that generates paragraphs which appear similar to those in the corpus of Noam Chomsky's linguistic works, but are humorously devoid of any meaning, by combining at random phrases taken from Chomsky's actual works.

That is, the alleles in the offspring are a random sample of those in the parents.