# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# PDF

PDF[dist,x]
gives the probability density function for the symbolic distribution dist evaluated at x.

PDF[dist,{x1,x2,}]
gives the multivariate probability density function for a symbolic distribution dist evaluated at {x1,x2,}.

PDF[dist]
gives the PDF as a pure function.

## DetailsDetails

• For discrete distributions, PDF is also known as a probability mass function.
• For continuous distributions, PDF[dist,x] dx gives the probability that an observed value will lie between x and x+dx for infinitesimal dx.
• For discrete distributions, PDF[dist,x] gives the probability that an observed value will be x.
• For continuous multivariate distributions, PDF[dist,{x1,x2,}]dx1 dx2 gives the probability that an observed value will lie in the box given by the limits xi and xi+dxi for infinitesimal dxi.
• For discrete multivariate distributions, PDF[dist,{x1,x2,}] gives the probability that an observed value will be {x1,x2,}.

## ExamplesExamplesopen allclose all

### Basic Examples  (4)Basic Examples  (4)

The PDF of a univariate continuous distribution:

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The PDF of a univariate discrete distribution:

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The PDF of a multivariate continuous distribution:

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The PDF for a multivariate discrete distribution:

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