What is the difference between density and distribution?

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SUMMARY

The discussion clarifies the distinction between density and distribution in the context of probability and energy. A distribution quantifies the total amount over a specified region, while density requires integration to determine the total amount over that same region. In probability theory, the cumulative distribution function (CDF) is often used to express the distribution, indicating the probability of a variable falling within a certain range. The relationship between density and distribution is further defined, with density being the exterior derivative of the distribution.

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  • Understanding of probability theory concepts
  • Familiarity with cumulative distribution functions (CDF)
  • Basic knowledge of integration techniques
  • Concept of exterior derivatives in calculus
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loom91
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Hi,

What is the difference between a density and a distribution? As in probability distribution and probability density, or energy distribution and energy density. Thanks.

Molu
 
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A distribution is a gadget that tells you how much there is over any region of space.

A density is a gadget you have to integrate in order to find out how much there is over any region of space.


Incidentally, in the probability case, we will often define the distribution in terms of a "cumulative distribution function": we use p(x) to tell how much there is over the interval (-infinity, x).

(Or maybe it's (-infinity, x]. I can't remember)
 
You mean the density is the exterior drivative of the distribution? Can you give an example?
 

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