Cauchy Command

Cauchy[ <Median>, <Scale>, x ]

Creates probability density function (pdf) of Cauchy distribution.

Cauchy[ <Median>, <Scale>, x, <Boolean Cumulative>]

If Cumulative is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution.

Cauchy[ <Median>, <Scale>, <Variable Value> ]

Calculates the value of cumulative distribution function of Cauchy distribution at Variable Value v, i.e. the probability P(X ≤ v) where X is a random variable with Cauchy given by parameters Median and Scale.

Note: Returns the probability for a given x-coordinate's value (or area under the Cauchy distribution curve to the left of the given x-coordinate).

CAS Syntax

Cauchy[ <Median>, <Scale>, <Variable Value> ]

Calculates the value of cumulative distribution function of Cauchy distribution at Variable Value v, i.e. the probability P(X ≤ v) where X is a random variable with Cauchy given by parameters Median and Scale.

Example:

Cauchy[1, 2, 3] yields \frac{3}{4}.