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Density (of Probability)

Density Functions:

A probability density function or curve is a non-negative function Math image ( Math image ) that describes the distribution of a continuous random variable Math image . If Math image is known, then the probability Math image that a value of the variable Math image is within an interval Math image is described by the following integral

Glossary Math

For very small intervals Math image , where Math image is a small value, the relation is simpler:

Glossary Math

The reason for using probability density instead of probability itself is the following: Continuous variables, in contrast to discrete random variables cannot be described by the probability of particular values of Math image because there are infinitely many possible values and they are not countable. This makes the probability of any particular value equal to zero. For example, the probability that the body weight of an individual is exactly Math image kilogram is practically zero, but the probability that body weight is within the interval Math image kg is a measurable quantity.

Note that the probability density function is the curve itself, and the probability is the area under the curve.

See also: joint probability density , marginal density , and short course Basic Concepts in Probability and Statistics.

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