Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2 < sup > n </ sup >/ 1.

Assuming that an information source produces random variables with an associated probability density function, the probability that the random variable falls within a particular quantization interval is given by

Assuming athletic careers are partly based on random factors, attributing this to a " jinx " rather than regression, as some athletes reportedly believed, would be an example of committing the regression fallacy.

Assuming that the online casino is using an appropriately programmed random number generator, table games like blackjack have an established house edge.

Assuming the missing data are missing at random this results in an estimate for the covariance matrix which is unbiased.

Assuming a full-scale sine wave signal ( that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal ), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level and uniform distribution.

Assuming zero empirical mean ( the empirical mean of the distribution has been subtracted from the data set ), the principal component w < sub > 1 </ sub > of a data set X can be defined as:

Assuming that the magnitude of each component is uncorrelated and normally distributed with equal variance, then the overall wind speed ( vector magnitude ) will be characterized by a Rayleigh distribution.

Assuming a uniform distribution does well, and it is possible to calculate inferences about unseen tiles that marginally improves on that assumption.

Assuming for simplicity a uniform distribution of branch targets, 0. 5, 1. 5, and 3. 5 instructions fetched are discarded, respectively.

Assuming a sinusoidal distribution, the current impressed by this voltage differential is given by:

Assuming the fluctuations are small, the probability distribution function can be expressed through the second differential of the entropy

Assuming there are no side entries, on the distribution shown East must duck once to prevent declarer from running the suit.

Assuming a Gaussian distribution of particle positions and impulses, a charged particle beam ( or a bunch of the beam ) is characterized by

Assuming a constant rate of mutation, Luria hypothesized that if mutations occurred after and in response to exposure to the selective agent, the number of survivors would be distributed according to a Poisson distribution with the mean equal to the variance.

Assuming that the signal value is in the range of one step of the quantized value with an equal distribution, the root mean square value of this quantization noise is

Assuming thermal equilibrium between the anode surface and the transpiring argon, the gas enthalpy rise through the anode was calculated according to the relation Af whereby the specific heat of argon was taken as Af.

Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

), the total human biomass is the average weight multiplied by the current human population of approximately 6. 5 billion ( see, e. g., ): Assuming 60 – 70 kg to be the average human mass ( approximately 130 – 150 lb on the average ), an approximation of total global human mass of between 390 billion ( 390 × 10 < sup > 9 </ sup >) and 455 billion kg ( between 845 billion and 975 billion lb, or about 423 million – 488 million short tons ).

Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently.

Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, then:

Assuming that the heat of fusion is temperature-independent and ignoring additional transition temperatures between different solid phases the equation

* Assuming no further changes in the copyright law, all sound recordings fixed between February 15 and December 31, 1972 will enter public domain in the United States:

Assuming that quantized values of L are equally spaced, the spacing between neighboring energies is

Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.

Assuming the validity of Bell's theorem, any deterministic hidden-variable theory which is consistent with quantum mechanics would have to be non-local, maintaining the existence of instantaneous or faster-than-light relations ( correlations ) between physically separated entities.

Assuming bus commuters do not care about the color of the bus, consumers are expected to choose between bus and car still with equal probability, so the probability of car is still 0. 5, while the probabilities of each of the two bus types is 0. 25.

Assuming that all three concepts of mass are equivalent the gravitational interactions between masses of arbitrary sign can be explored.

* Assuming that the constitutional monarchy was in fact an ideal held throughout all ages of the past, despite the observed facts of British history and the several power struggles between monarchs and parliaments ;

Assuming that games and routine social acts have differentiated social positions, and that these positions create our cognitive perspectives, then it might be that by moving between roles in a game ( eg between hiding and seeking or buying and selling ) we come to learn about the perspective of the other.

Assuming the legs are recovered with a relative speed between leg and body which amounts to the same as the relative speed between water and body, the legs must be kicked back with five times the mean velocity of the swimmer.

Assuming the spacing between two ions is a, the potential in the lattice will look something like this:

Assuming that one gets the relation between the Townsend coefficients by putting ( 4 ) into ( 3 ) and transforming:

It is sometimes called a tickler oscillator because the feedback needed to produce oscillations is provided using a tickler coil ( T in the circuit diagram ) via magnetic coupling between coil L and coil T. Assuming the coupling is weak, but sufficient to sustain oscillation, the frequency is determined primarily by the tank circuit ( L and C in the illustration ) and is approximately given by.

Assuming Winston did not have the irradiation treatment done, it could have taken place any time between 1955 ( when Winston sold it ) and 1971, the year it was offered at auction.

Assuming that non-members take reasonable precautions and adjusting activities to the association's prohibition of their enforcing their own rights, the association is required to raise the non-member above his actual position by an amount equal to the difference between his position on an indifference curve he would occupy were it not for the prohibition, and his original position.

Assuming the source to be " rotationally invariant " ( to produce all possible states λ with equal probability ), the probability of a given type of coincidence will clearly be proportional to the corresponding area, and these areas will vary linearly with the angle between a and b. ( To see this, think of an orange and its segments.

Assuming such a statistical ensemble consists of an overall collection of N microscopic states, the ensemble is constructed so that the proportion p < sub > i </ sub >/ N of members of the ensemble which are in microscopic state i is proportional to the probability, over time, of finding the real-world system in that microscopic state i. Thus the ensemble is an imaginary static collection of microscopic states created to mirror the statistics of the successive fluctuations of the macroscopic physical system which is being modeled.

Assuming every piece of regulation to be burdensome by default, the Directive required member states to justify all existing legislation on the grounds that it was non-discriminatory, necessary and proportional.

Assuming the formation of the wavefunctions is a fast process compared to the scattering between states, the time independent solutions to the Schrödinger equation may be applied and the system can be modelled using rate equations.

Assuming A is true is therefore enough to guarantee that B is true regardless of the truth of statement B.

Assuming that all members of parliament are present, all that is requried to win is 141 votes, regardless of the house of origin.