Probability Density

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probability density

[‚präb·ə′bil·əd·ē ‚den·səd·ē]

(quantum mechanics)

The square of the absolute value of the Schrödinger wave function for a particle at a given point; gives the probability per unit volume of finding the particle at that point.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Probability Density

The probability density of a random variable X is a function p(x) such that for any a and b the inequality a < X < b has probability equal to

For example, if X has a normal distribution,

If p(x) is continuous, the probability of the inequality x < X < x + dx is approximately equal to p(x) dx for sufficiently small dx. The probability density always satisfies the conditions

The probability density p(x₁,…, x_s) for several random variables X₁, X₂,…, X_s is defined in a similar manner and is called the joint probability density. Thus, for any a_i and b_i, the probability that the inequalities a₁ < X₁ < b₁,…, a_s < X_s < b_s are simultaneously satisfied is equal to

If the random variables X₁, X₂,…, X_s have joint probability density, they will be independent if, and only if, their joint probability density is the product of the probability densities of each of them.

References in periodicals archive ?

Specifically, it is concluded that the SE of the plastic-damage variable dr (Figure 8(a)) is caused by progressive accumulation of the plasticity and damage for SCC samples with different yield and damage thresholds (probability densities) displayed in Figure 7(a).

Stochastic Constitutive Relationship of Self-Compacting Concrete under Uniaxial Compression

Butler and Davies [35] applied a correction of this kind to the implied probability densities in the interest rate contracts on three-month Euro-sterling.

The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index

Our current effort in this paper is to further explore the limiting behavior of the process [x.sup.[epsilon], [delta]](x) by constructing asymptotic expansions of its probability densities, which are associated with the adjoint operator [L.sup.*].

SINGULARLY PERTURBED MULTI-SCALE SWITCHING DIFFUSIONS

The system state is described by probability densities of the numbers of molecules of different species.

Approximate Exponential Algorithms to Solve the Chemical Master Equation

The comparison of the probability densities for 8% RH at 27[degrees]C and 38[degrees]C is shown in Figure 5; the two environmental conditions have similar probability density distribution.

Dependence of ESD charge voltage on humidity in data centers: part III--estimation of ESD-related risk in data centers using voltage level extrapolation and Chebyshev's inequality

We know that all analyses to the multipactor discharge are based on an SEY model and the probability densities of the release velocity and angle of secondary electrons [10].

Multicarrier Multipactor Analysis Based on Branching Levy Walk Hypothesis

By numerical simulations, the probability densities p(a) of the amplitude of the original system (5) and of the slow system (12) are plotted in Figure 2.

The effect of high-frequency parametric excitation on a stochastically driven pantograph-catenary system

In classical mechanics, there are no equations that describe the evolution of the probability densities P(r, t) (or P(p,t), where p is momentum); only joint probability densities, [W.sub.cl](p,r,t), can be expressed by the Liouville equation.

Molecular tomography of the quantum state by time-resolved electron diffraction

Then the joint probability density function is a product of the individual probability densities

Detection of the consistency of two speech signals using pitch periods/Robustne detektor uhtlase jaotusega miira tarvis

In the context of fractional diffusion, the function [M.sub.[beta]/2](z) belongs to the Wright type of probability densities characterized by the similarity variable z = [absolute value of x]/[square root of [D.sub.f]][t.sup.[beta]/2], where [D.sub.f] is the fractional diffusion coefficient, with [[integral].sup.[infinity].sub.0 ] [M.sub.[beta]/2](z)dz = 1.

Time fractional Schrodinger equation revisited

In the classical regime the sum of probability densities |ps1|2+|ps2|2 of the detached-electron from individual atoms is equal to the probability density |ps|2from the diatomic molecule.

CLASSICAL LIMIT IN THE PHOTO-DETACHMENT OF A DIATOMIC ANION: A TWO-CENTER MODEL APPROACH