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.

Details

  • 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,}.

Examples

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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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Scope  (22)

Applications  (10)

Properties & Relations  (9)

Possible Issues  (2)

Neat Examples  (3)

See Also

CDF  SurvivalFunction  HazardFunction  Quantile  Probability  Expectation  Mean  BinCounts  Histogram

Tutorials

Introduced in 2007
(6.0)
| Updated in 2010
(8.0)