### probability density function

**(PDF)**
(shows probability of taking a particular value from a continuous range)

A **probability density function** (**PDF**)
is a function on a continuous random variable
that gives the relative likelihood of the
variable taking the given value.
If a function shows the relative density
at each possible value of the random variable,
but the sum of the probabilities does not
equal one, then it can be referred to as
an **unnormalized PDF** and the equivalent
**normalized PDF** (**NPDF** or **N-PDF**) can be derived by
taking the unnormalized PDF and incorporating
an (additional) division by the area under the curve.

A **continuous random variable** is a value that
can have any value over an interval.
For example, if you have observed the widgets
a factory produces randomly vary in length over an inch,
but always between 10 and 11 inches, then you can
model the length as a random variable, and perhaps
discover a function (a PDF) over the interval
of real numbers from 10 to 11 that describes
the probability of each corresponding length
in inches.

Similarly, a **probability mass function** (**PMF**)
is like a PDF except that rather than mapping into
a continuous random variable, it maps into a
**discrete random variable**, i.e., a finite number of values.

(*mathematics,statistics,function*)
http://en.wikipedia.org/wiki/Probability_density_function

**Referenced by:**

Bayesian statistics

conditional stellar mass function (CSMF)

dense core mass function (DCMF)

Gaussian function

halo mass function

initial mass function (IMF)

luminosity function (LF)

Maxwell-Boltzmann distribution

planetary nebula luminosity function (PNLF)

index