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( Note that the Cauchy distribution and this spectrum differ by scale factors.
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Note and Cauchy
Note that not every probability distribution has a defined mean ; see the Cauchy distribution for an example.
Note also that a factor consisting of a sum where both types of variables are involved ( e. g. a factor of the form ) cannot be factorized in this fashion ( except in some cases where occurring directly in an exponent ); this is why, for example, the Cauchy distribution and Student's t distribution are not exponential families.
Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically efficient as the maximum likelihood estimator ; however, the maximum likelihood estimate is difficult to compute, leaving the truncated mean as a useful alternative.
Note also that this implies that the Pearson type VII distribution subsumes the standard Student's t-distribution and also the standard Cauchy distribution.
Note and distribution
Note that the two-sample test checks whether the two data samples come from the same distribution.
( Note that for a discrete distribution the sample skewness may be undefined ( 0 / 0 ), so its expected value will be undefined.
Note that personal ( per capita ) income distribution, given in this table, is not exactly comparable with household income distribution, given in the previous table, because poor households tend to have more members.
Note that the terms indicate the origin of the groups, not their modern distribution: the water deer, for example, is a New World species but is found only in China and Korea.
Note that under either hypothesis, the distribution of the data is fully specified ; there are no unknown parameters to estimate.
Note that this definition of the negative binomial distribution does not easily generalize to a positive, real parameter r.
Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement.
Note that both types of predictive distributions have the form of a compound probability distribution ( as does the marginal likelihood ).
Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).
Note how the equation above reduces to that of the univariate normal distribution if is a matrix ( i. e. a real number ).
Note that knowing that alters the variance, though the new variance does not depend on the specific value of a ; perhaps more surprisingly, the mean is shifted by ; compare this with the situation of not knowing the value of a, in which case x < sub > 1 </ sub > would have distribution
Note that the acceptance ratio indicates how probable the new proposed sample is with respect to the current sample, according to the distribution.
Note that the t-distribution ( red line ) becomes closer to the normal distribution as increases.
Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a normal distribution, but this is not correct.
Note that although we are looking at success / failure, the data are not accurately modeled by the binomial distribution, because the probability of success on each trial is not the same, as the size of the remaining population changes as we remove each marble.
( Note that this particular case of the Bernoulli distribution has the lowest possible excess kurtosis ; this can be proved by Jensen's inequality as follows.
Note that the higher the polytropic index, the more condensed at the centre is the density distribution.
Note that although this model is termed a " Gaussian chain ", the distribution function is not a gaussian ( normal ) distribution.
Note that a " stationary process " is not the same thing as a " process with a stationary distribution ".
Note also that the function A ( θ ) or equivalently g ( θ ) is automatically determined once the other functions have been chosen, and assumes a form that causes the distribution to be normalized ( sum or integrate to one over the entire domain ).
Note and spectrum
( Note: bandwidth is proportional to where = bit time ) Therefore, the bandwidth of the data signal is and the bandwidth of the spread spectrum signal is.
Note that historical opinions fall on a spectrum, rather than into tightly defined camps.
Note that the approximate point spectrum and residual spectrum are not necessarily disjoint ( however, the point spectrum and the residual spectrum are ).
Note that virtually all the light produced is in the blue to green region of the spectrum below about 565 nanometers, accounting for the bluish color of sootless hydrocarbon flames.
Note, however, that the spectrum and projective spectrum are still T < sub > 0 </ sub > spaces: given two points P, Q, which are prime ideals of A, at least one of them, say P, does not contain the other.
Note: is not same as the one mentioned before where it refers to the width of the spectrum.
Note that the quantity being traced over is an element of the gauge Lie group and the trace is really the character of this element with respect to one of the infinitely-many irreducible representations, which implies that the operators don't need to be restricted to the " trace class " ( thus with purely discrete spectrum ), but can be generally hermitian ( or mathematically: self-adjoint ) as usual.
Note that the designation " Right Opposition " refers to the position of this movement relative to the other Communist movements on the traditional spectrum.
( Note that this lens is designed for astronomy, so one of the 3 wavelengths is outside the visible spectrum.
Note this equation's spectral and time dependence — may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample.
Note that while two forms of the same spectrum are presented in the figure, most EPR spectra are recorded and published only as first derivatives.
Note again that the lines in this spectrum are first derivatives of absorptions.
The sound is perceived as louder than it actually is ; sound designer Gary Rydstrom explains that, " from a technical standpoint, ' Deep Note ' just feels loud because it has a spectrum of frequencies that grows from small to large.
Note that the spectrum does not represent either a chronological or technical order ; the Northrop YB-49 | YB-49 ( 4 ), representing a true flying wing, actually predates all other depicted aircraft, while the " conventional " Boeing 757 ( 1 ) is a relatively new and technologically advanced aircraft, and the X-48 ( 2 ) is the most recently developed.
Note that there was a special emphasis on the adding of formal is-a relationships to the spectrum which seems to have been dropped.
Note and differ
( Note: Dates of capitulation differ slightly depending on source ).
Note that sociologists give these words precise definitions which differ from how they are commonly used.
Note: Requirements for global and tactical high-performance equipment may differ.
Note that the line-coded signal and a signal produced at a terminal may differ, thus requiring translation.
Note that this is a list of features of the main forms of Valencian as a group of dialectal varieties that differ from those of other Catalan dialects, particularly from the Central variety of the language.
File: Terracotta pmorgan. jpg | Note how the faces of these two soldiers differ from each other.
Note that the electrical levels differ between AES / EBU and S / PDIF.
Note: Some home console versions of NBA Jam were coded later than others, and as a result of real-life roster changes or in the cases of Charles Barkley and Shaquille O ' Neal, legal reasons, some rosters differ from version to version.
Note that because the various definitions of " open standard " differ in their requirements, the standards listed below may not be open by every definition.
Note that while " hue " in HSL and HSV refers to the same attribute, their definitions of " saturation " differ dramatically.
Note that high-resolution PCM ( DVD-Audio, HD DVD and Blu-ray Disc ) and DSD ( SACD ) may still technically differ at high frequencies.
Note: The dosage recommendations for glaucoma and epilepsy differ considerably from those for congestive heart failure, since the first two conditions are not dependent upon carbonic anhydrase inhibition in the kidney which requires intermittent dosage if it is to recover from inhibitory effect of the therapeutic agent.
Note that the antisymmetrized covariant derivative ∇< sub > u </ sub > v − ∇< sub > v </ sub > u, and the Lie derivative L < sub > u </ sub > v differ by the torsion of the connection, so that if a connection is symmetric, then its antisymmetrization is the Lie derivative.
Note that if we used the actual real-world probabilities, every security would require a different adjustment ( as they differ in riskiness ).
Note that the three-way flip is 75 % likely to work each time it is tried ( if all coins are heads or all are tails, which occurs 1 / 4 of the time, the flip is repeated until the results differ ), and does not require that " heads " or " tails " be called.
Note that this section refers to the English-language dub of Les Maîtres du temps, and certain details may differ from the original.
Note that some of the numbers are revised after initial publication of the report, which causes some of the numbers used in excerpted comparisons to differ from what was originally reported.
Note that the pronunciation and sometimes spelling of Gongadze's name may differ following the phonetics of different languages.
Note that for the last mission phase, trans-earth injection, fuel requirements differ depending on whether the Service Module Propulsion System ( SPS ) or the Lunar Module's Descent Engine ( DPS ) is used, however the required delta-v is the same for either burn.
Note that the normalization factor in front of the sum () and the sign of the exponent in ω are merely conventions, and differ in some treatments.
Note that the grades for flour are not standardized, so the same grade grains from different sources may differ in size slightly.
Note that approved indications differ by country.
Note that definitions of the Fourier transform differ, and in particular
Note: Although " Mariah " and " Maria " differ by one letter, proper pronunciation is " mah-RYE-ah.
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