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For and probability

For him, " probability " means a higher chance of occurring, and brings about a higher degree of subjective expectation in the viewer.

* For the frequentist a hypothesis is a proposition ( which must be either true or false ), so that the frequentist probability of a hypothesis is either one or zero.

For objectivists, probability objectively measures the plausibility of propositions, i. e. the probability of a proposition corresponds to a reasonable belief everyone ( even a " robot ") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency.

For subjectivists probability corresponds to a ' personal belief '.

For example, Hacking writes " And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption.

For example, the probability that an alpha particle striking a beryllium target will produce a neutron can be expressed as the equivalent cross section of beryllium for this type of reaction.

For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked ( i. e., rejected ) due to all circuits being in use ( a GoS of 0. 01 ), which becomes the target probability of call blocking, P b , when using the Erlang B formula.

For example, if one flips a fair coin 21 times, then the probability of 21 heads is 1 in 2, 097, 152 ( above ).

For most types of hashing functions the choice of the function depends strongly on the nature of the input data, and their probability distribution in the intended application.

For any information rate R < C and coding error ε > 0, for large enough N, there exists a code of length N and rate ≥ R and a decoding algorithm, such that the maximal probability of block error is ≤ ε ; that is, it is always possible to transmit with arbitrarily small block error.

For instance, if a particle is in a state | ψ ⟩, the probability of finding it in a region of volume d 3 x surrounding some position x is

For example, consider a model which gives the probability density function of observable random variable X as a function of a parameter θ.

For example, the result of a significance test depends on the probability of a result as extreme or more extreme than the observation, and that probability may depend on the design of the experiment.

For a discrete probability function f ( y ), let y i , i = 1 to n, be the points with non-zero probabilities indexed in increasing order ( y i < y i + 1 ).

For a probability distribution, the mean is equal to the sum or integral over every possible value weighted by the probability of that value.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated.

For calling to have a positive expectation, Alice must believe the probability of her opponent having a weak hand is over 40 percent.

For example, seven shuffles of a new deck leaves an 81 % probability of winning New Age Solitaire where the probability is 50 % with a uniform random deck ( Mann, especially section 10 ).

For and density

For this reason, he says, the density of the universe always remains the same even though the galaxies are zooming away in all directions.

For incompressible flows, density remains constant.

For example, it also predicts the variation of the particle density in a gravitational field with height, if.

For alternating currents, especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.

For more massive stars, electron degeneracy pressure will not keep the iron core from collapsing to very great density, leading to formation of a neutron star, black hole, or, speculatively, a quark star.

For determining the density of a liquid or a gas, a hydrometer or dasymeter may be used, respectively.

For example, the density of water increases between its melting point at 0 ° C and 4 ° C ; similar behavior is observed in silicon at low temperatures.

For comparison, the energy density of TNT is 4. 7 megajoules per kilogram, and the energy density of gasoline is 47. 2 megajoules per kilogram.

For a given energy in a given volume, there is an upper limit to the density of information ( the Bekenstein bound ) about the whereabouts of all the particles which compose matter in that volume, suggesting that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of fundamental particles.

For a given mass of fissile material the value of k can be increased by increasing the density.

For the density of the observable universe of about 4. 6 × 10 − 28 kg / m 3 and given the known abundance of the chemical elements, the corresponding maximal radiation energy density of 9. 2 × 10 − 31 kg / m 3 , i. e. temperature 3. 2K.

For example the central convex pentagon in the center of a pentagram has density 2.

For a population of discrete values, or for a continuous population density, the th-quantile is the data value where the cumulative distribution function crosses.

For example, if one begins with the Lagrangian density

For example, the reduced density matrix of for the entangled state

For n independent and identically distributed continuous random variables X 1 , X 2 , ..., X n with cumulative distribution function G ( x ) and probability density function g ( x ) the range of the X i 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 1 , X 2 , ..., X n with cumulative distribution functions G 1 ( x ), G 2 ( x ), ..., G n ( x ) and probability density functions g 1 ( x ), g 2 ( x ), ..., g n ( x ), the range has cumulative distribution function

For a given core material, the loss is proportional to the frequency, and is a function of the peak flux density to which it is subjected.

For customers in these rural and low density suburban areas fixed wireless ISPs provide a unique service.

For example, an ice cube, with a relative density of about 0. 91, will float.

For example SG ( 20 ° C / 4 ° C ) would be understood to mean that the density of the sample was determined at 20 ° C and of the water at 4 ° C.

For and function

For it is clear that the total number of ordinary intersections of C and Af must be even ( otherwise, starting in the interior of C, Af could not finally return to the interior ), and the center of rotation at T is the argument of the function, not a value.

For a statement of costs per kilowatt-hour would ignore the fact that many of these costs are not a function of kilowatt-hour output ( or consumption ) of energy.

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.

: For any set X of nonempty sets, there exists a choice function f defined on X.

: For any set A, the power set of A ( with the empty set removed ) has a choice function.

: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

For a reader to assign the title of author upon any written work is to attribute certain standards upon the text which, for Foucault, are working in conjunction with the idea of " the author function ".

For example, the parent function y = 1 / x has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant.

For small values of m like 1, 2, or 3, the Ackermann function grows relatively slowly with respect to n ( at most exponentially ).

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For example, for the function

For example the arctangent function satisfies

For example, the function has a horizontal asymptote at y = 0 when x tends both to −∞ and +∞ because, respectively,

For example, the function has

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

For instance, division of real numbers is a partial function, because one can't divide by zero: a / 0 is not defined for any real a.

For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero.

For example, methods to locate a gene within a sequence, predict protein structure and / or function, and cluster protein sequences into families of related sequences.

For each K, the function E K ( P ) is required to be an invertible mapping on

For integer order α = n, J n is often defined via a Laurent series for a generating function:

For example, kinship and leadership function both as symbolic systems and as social institutions.

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