Cauchy Command

Cauchy( <Median>, <Scale>, <Variable value> ): Calculates the value of the cumulative density function (cdf) at the given variable value v of a Cauchy distribution, that is the probability P(X≤v) where X is a random variable of a Cauchy distribution of given parameters median and scale.

Cauchy(1, 2, 3) yields 0.75 in the Algebra View and \(\frac{3}{4}\) in the CAS View.

This syntax returns the probability for a given value, that is the area under the Cauchy distribution curve to the left of the given x-coordinate.

Cauchy( <Median>, <Scale>, <Variable value>, <Boolean Cumulative>): If Cumulative is true, calculates the value of a cumulative distribution function of a Cauchy distribution at variable value, otherwise it calculates the value of the probability density function (pdf) at variable value of the given Cauchy distribution of parameters median and scale.
Cauchy( <Median>, <Scale>, x, <Boolean Cumulative>): If Cumulative is true, creates the cumulative distribution function of a Cauchy distribution, otherwise creates the probability density function of the given Cauchy distribution of parameters median and scale.