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Probability density function (3277 bytes)
1: ...m will resemble the random variable's probability density (assuming that the variable is sampled sufficient... 3: ...e]] function '''R''' → '''R''' such that the probability of the interval [''a'', ''b''] is given by 7: ... is the probability density of a suitably defined probability distribution. 9: ... standard [[normal distribution]] has probability density 13: ...and its distribution admits a probability density function ''f''(''x''), then the [[expected value]] of ''X'... Probability mass function (2398 bytes) 1: ...et of possible values of the random variable is a probability. 5: ...;''S'' ⊆ '''R'''. Then the probability mass function ''f''<sub>''X''</sub>(''x'') for ''X'... 7: ...ould never take; indeed, it assigns such values a probability of zero. (Alternatively, think of Pr(''X''... 9: ... derivative is zero, just as the probability mass function is zero at all such points. 13: ...andom variable]]), and hence the probability mass function is Probability-generating function (6060 bytes) 1: ...] of the random variable. Probability-generating functions are often employed for their succinct descriptio... 5: ...''0,1, ...''}, then the <i>probability-generating function</i> of ''X'' is defined as: 7: ...to distinguish between the probability-generating functions of several random variables. 13: ...us of convergence]] of any probability-generating function must be at least 1, by [[Abel's theorem]] for pow... 19: 1. The probability mass function of ''X'' is recovered by taking [[derivative]]s o... Density 21.5 (7117 bytes) 1: ...e]] for the premiere of his platinum flute, the [[density]] of platinum being 21.5 grammes per cubic centim... 3: ...e's Sean Hickey says, "According to the composer, Density 21.5 is based on two [[melody|melodic]] ideas -- ... 7: ...ough this [[ambiguity]], this perpetual change of function, that the composition unfolds. This is what the c... 11: ...sub>1</sub>. And here, in the last two notes of ''Density 21.5'' we at last find b paired with its tritone ... 13: ...' to the harmonic structure of the piece, and its function in articulating and clarifying the formal design,... Density (7342 bytes) 1: :''For other meanings of density, see [[density (disambiguation)]]'' 3: ...ty, the higher its mass per volume. The ''average density'' of an object equals its total mass [[division|d... 5: The '''[[SI]] unit''' of density is the [[kilogram per cubic metre]] ('''[[kilogra... 11: ''ρ'' is the object's density (measured in kilograms per cubic metre) 17: ==Various types of density== Torque density (1626 bytes) 1: ... expressed in units of torque per volume. Torque density is a system [[property]] since it depends on the ... 3: ... be several types of devices that can perform the function of an existing component that must be replaced. T... 6: In [[SI|SI units]], torque density is expressed in [[joule]]s per [[cubic metre]] or... 9: In [[U.S. customary units]], torque density is expressed in [[foot-pound|foot-pounds force]] ... Force density (577 bytes) 1: ...ic force]] within the bulk of a [[fluid]]. Force density is represented by the symbol '''f''', and given b... 9: Thus, the force density at a point in a fluid determines the [[accelerati... Density (disambiguation) (442 bytes) 3: * [[Density]], treating mass-density in the physical sciences. 4: * '''Charge density''' is the [[electric charge]] per unit area or pe... 5: * [[Population density]] 6: * [[Probability density function]] 7: * [[Schnirelmann density]] in [[number theory]] Spectral density (1436 bytes) 1: ...nsity''', or more correctly the '''power spectral density''' (PSD) of a given [[bandwidth]] of [[electromag... 3: '''Spectral density''' is usually expressed in [[watt]]s per [[hertz]... 5: ...d energy spectral densities. The energy spectral density is defined as 15: ...may not exist. Thus we define the power spectral density as the --> 24: * [[Window function]]. Electron density (2106 bytes) 1: '''Electron density''' is the measure of the [[probability]] of an [[electron]] being present at a specific ... 3: ...[[haemoglobin]] and [[chlorophyll]]) the electron density covers an entire region, i.e., in benzene they ar... 7: ...nt the delocalisation of areas where the electron density is higher next to the single bonds (e.g., the whi... Double density (547 bytes) 1: '''Double Density''' usually refers to a physical format in a [[mag... 3: In 3.5" [[Floppy disk]]s double density marks a disk format that uses 9 sectors of 512 [[... 5: ...ch doubles the capacity and bit density of double density. 7: The term double density can also be applied to magnetic tapes. 9: [[de:Double Density]] Density estimation (1003 bytes) 1: In [[probability]] and [[statistics]], 2: ...nobservable density function is thought of as the density according to which a large population is distribu... 4: A variety of approaches to density estimation are used, including [[Parzen window]]s... 6: Here is an [[illustration of density estimation]]. 12: * D.W. Scott. ''Multivariate Density Estimation. Theory, Practice and Visualization''.... Nuclear density (141 bytes) 1: ...], about 1018 kg/m³; [[neutron stars]] reach this density. Area density (231 bytes) 1: The '''area density''' of a two-dimensional object is calculated as t... Density of states (512 bytes) 1: ... are in some material. It is often expressed as a function ''N(E)'' of the [[internal energy]] ''E''. It is ... Density altitude (457 bytes) 1: ...ir|air density]] would be equal to the actual air density at the place of observation. 3: ...air density. Thus in hot and humid conditions the density altitude at a particular location may be signific... Density of air (3858 bytes) 1: .../sup>. varying with pressure and temperature. Air density and [[air pressure]] decrease with increasing alt... 5: The formula for the density of air is given by: 9: where ''ρ'' is the air density, ''p'' is pressure, ''R'' is the gas constant, an... 16: ...ssure]] (0 °C and 101.325 kPa), dry air has a density of ρ<sub>STP</sub> = 1.293 kg/m<sup>3</sup>). 17: ...nd pressure (25 °C and 100 kPa) dry air has a density of ρ<sub>SATP</sub> = 1.168 kg/m<sup>3</sup>)... Density state (3183 bytes) 1: A '''density [[matrix (math)|matrix]]''', or '''density operator''', is used in [[quantum theory]] to des... 2: ...mechanical analogue to a [[phase-space density]] (probability distribution of position and momentum) 3: ...or a statistical description via [[density matrix|density matrices]] arises because it is not possible to d... 5: Typical situations in which a density matrix is needed include: a quantum system in the... 6: ...ere each individual system must be described by a density matrix even though the complete system may be in ... Optical density (559 bytes) 1: '''Optical density''' (OD): For a given [[wavelength]], an expressi... 3: ''Note 1:'' Optical density is expressed by log<sub>10</sub>(1/''T'' ) where ... 5: ''Note 2:'' The higher the optical density, the lower the transmittance. 7: ...ss]] expressed in decibels, ''e.g.'' , an optical density of 0.3 corresponds to a transmission loss of 3 [[... Schnirelmann density (7717 bytes) 2: In [[mathematics]], the '''Schnirelmann density''' of a [[sequence]] of numbers is a way to measu... 4: ...r intuitive notion. This is what the Schnirelmann density does. 7: The Schnirelmann density of a set of natural numbers is defined as follows 10: ...eding <math>n</math>. The '''Schnirelmann natural density''' of <math>A</math> is defined as: 18: ...y</math>, which might not exist. The Schnirelmann density, on the other hand, is always defined.
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