Built-in Mathematica Symbol

PDF

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

PDF[dist]
gives the PDF as a pure 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.

The PDF of a normal distribution with zero mean and unit standard deviation:

The PDF of a hypergeometric distribution:

The PDF of a Poisson distribution as a pure function:

The PDF of a normal distribution with zero mean and unit standard deviation:

The PDF of a hypergeometric distribution:

The PDF of a Poisson distribution as a pure function:

Obtain exact numeric results:

Obtain a machine-precision result:

Obtain a result at any precision for a continuous distribution:

Obtain a result at any precision for a discrete distribution with inexact parameters:

Plot the PDF for a standard normal distribution:

Plot the PDF for a Poisson distribution:

The integral or sum over the support of the distribution is unity:

Integrating the PDF gives the CDF for continuous distributions:

Summing the PDF gives the CDF for discrete distributions:

The integral or sum of a function times the PDF is the ExpectedValue of the function:

Substitution of invalid values into symbolic outputs gives results that are not meaningful: