Difference between revisions of "Cauchy Command"
From GeoGebra Manual
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;Cauchy[ <Median m>, <Scale s>, x, <Boolean Cumulative>] | ;Cauchy[ <Median m>, <Scale s>, x, <Boolean Cumulative>] | ||
:If ''Cumulative'' is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution. | :If ''Cumulative'' is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution. | ||
| − | ;Cauchy[ <Median m>, <Scale s>, <Variable Value v> ]: Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Cauchy given by parameters ''m, s''. | + | ;Cauchy[ <Median m>, <Scale s>, <Variable Value v> ] |
| − | :{{ | + | :Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Cauchy given by parameters ''m, s''. |
| − | ==CAS | + | :{{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== | ||
In [[CAS View]] only following syntax is supported: | In [[CAS View]] only following syntax is supported: | ||
;Cauchy[ <Median m>, <Scale s>, <Variable Value v> ] | ;Cauchy[ <Median m>, <Scale s>, <Variable Value v> ] | ||
| − | : Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Cauchy given by parameters ''m, s''. | + | :Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Cauchy given by parameters ''m, s''. |
| − | :{{example| 1=<div><code><nowiki>Cauchy[1, 2, 3]</nowiki></code> | + | :{{example| 1=<div><code><nowiki>Cauchy[1, 2, 3]</nowiki></code> yields''<math>\frac{3}{4}</math>''.</div>}} |
Revision as of 11:49, 7 September 2011
- Cauchy[ <Median m>, <Scale s>, x ]
- Creates probability density function (pdf) of Cauchy distribution.
- Cauchy[ <Median m>, <Scale s>, x, <Boolean Cumulative>]
- If Cumulative is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution.
- Cauchy[ <Median m>, <Scale s>, <Variable Value v> ]
- Calculates the value of cumulative distribution function of Cauchy distribution at v, i.e. the probability P(X≤v) where X is a random variable with Cauchy given by parameters m, s.
- 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
In CAS View only following syntax is supported:
- Cauchy[ <Median m>, <Scale s>, <Variable Value v> ]
- Calculates the value of cumulative distribution function of Cauchy distribution at v, i.e. the probability P(X≤v) where X is a random variable with Cauchy given by parameters m, s.
- Example:
Cauchy[1, 2, 3]yields\frac{3}{4}.
