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 It might be outdated or ideologically biased.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.

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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.

Fractional Degrees of Freedom in Statistics

The probability density function of the production of matrix asphalt materials is shown in Figure 2.

Reliability Evaluation of Pavement Life-Cycle Assessment Model

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.

An Assessment of GCM Performance at a Regional Scale Using a Score-Based Method

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.

A Renormalisation Group Approach to the Universality of Wigner's Semicircle Law for Random Matrices with Dependent Entries

We also apply the same result to the difference of the probability density function in Figure 2.

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

The probability density function of a normal distribution is given as follows [13]:

Researches on Damage Evolution and Acoustic Emission Characteristics of Rocks

We can express the probability density function [f.sub.[theta]](L) in terms of a Dirac function as

A Poisson-Gamma Model for Zero Inflated Rainfall Data

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.

Adaptive Resource Allocation Scheme for Micromotion Feature Extraction Based on Track-Before-Detect

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.

THE EFFECT OF THE STRUCTURAL INTERFACE OF THE RESONANCE TUNNELING DIODE ON ITS PERFORMANCE