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##

3.2.1 Transformation of probability densities

Given and a bijective mapping
; then

or

This relation holds for *any* kind of density.

__EXAMPLE:__
The spectral density of black body radiation
is usually written in terms of the angular frequency
:

If we prefer to give the spectral density in terms of the wave length
, we have

__EXERCISE:__
A powder of approximately spherical metallic grains is used for sintering.
The diameters of the grains obey a normal distribution with
and
. Determine
the distribution of the grain volumes.

** Next:** 3.2.2 Transformation Method
**Up:** 3.2 Other Distributions
** Previous:** 3.2 Other Distributions
* Franz J. Vesely Oct 2005*

See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001