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.

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.
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The probability density function of the production of matrix asphalt materials is shown in Figure 2.
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The probability density function of a normal distribution is given as follows [13]:
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The statistical variances and probability density distribution produced by random dispersion of vacancy defects are analyzed and discussed.
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