density function

Let X be a discrete random variable with sample space {x1,x2,}. Let pk be the probability of X taking the value xk.

The functionMathworldPlanetmath

f(x)={pkif x=xk0otherwise

is called the probability functionDlmfDlmfPlanetmath or density function.

It must hold:


If the density function for a random variable is known, we can calculate the probability of X being on certain interval:


The definition can be extended to continuous random variables in a direct way: The probability of x being on a given interval is calculated with an integral instead of using a summation:


For a more formal approach using measure theory, look at probability distribution function entry.

Title density function
Canonical name DensityFunction
Date of creation 2013-03-22 13:02:49
Last modified on 2013-03-22 13:02:49
Owner drini (3)
Last modified by drini (3)
Numerical id 12
Author drini (3)
Entry type Definition
Classification msc 60E05
Synonym probability function
Synonym density
Synonym probabilities function
Related topic DistributionFunction
Related topic CumulativeDistributionFunction
Related topic RandomVariable
Related topic DistributionDlmfPlanetmath
Related topic GeometricDistribution2