# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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 It might be outdated or ideologically biased.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,…, xs) for several random variables X1, X2,…, Xs is defined in a similar manner and is called the joint probability density. Thus, for any ai and bi, the probability that the inequalities a1 < X1 < b1,…, as < Xs < bs are simultaneously satisfied is equal to If the random variables X1, X2,…, Xs 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 ?
One of the options for describing the distribution law P is the probability density. By the given probability density or histogram it is possible to calculate or to estimate the parameters of the distribution law.
The probability density function of the production of matrix asphalt materials is shown in Figure 2.
According to the data ranges, we set the number of bins as 100; thus, we divided all of the data into 100 equal parts sequentially and then calculated the probability density of each size.
where [rho]' is the common probability density of the real diagonal terms and [rho]" is the common probability density of the real and imaginary parts of the off-diagonal terms.
We also apply the same result to the difference of the probability density function in Figure 2.
The probability density function of a normal distribution is given as follows :
We can express the probability density function [f.sub.[theta]](L) in terms of a Dirac function as
It can better characterize the spatial distribution of gray levels and can directly generate the probability density function by using images for subsequent registration.
The probability density function of cumulative energy I([y.sub.k]) can be calculated, respectively, under two different conditions: one is that only noise exists in the searching gate, the other is that target exists in the searching gate.
The statistical variances and probability density distribution produced by random dispersion of vacancy defects are analyzed and discussed.
Where m* is the band-edge effective mass, k is Boltzmann constant, T is the lattice absolute temperature, h is Plank constant divided by 2, Tu* Tu gives the tunneling probability density of the outgoing electron, F is Fermi energy level, l is energy of the electron associated with longitudinal wave vector of the electron in the conduction band, V is the applied voltage.

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