Difference between revisions of "TDistribution Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
{{command|cas=true|probability}}
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;TDistribution( <Degrees of Freedom>, x )
;TDistribution[ <Degrees of Freedom d>, x ]
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:Creates cumulative density function (cdf) of [[w:Student's t-distribution|t-distribution]] with given degrees of freedom.
:Creates probability density function (pdf) of [[w:Student's t-distribution|t-distribution]] with ''d'' degrees of freedom.
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;TDistribution( <Degrees of Freedom>, x, <Boolean Cumulative> )
;TDistribution[ <Degrees of Freedom d>, x, <Boolean Cumulative> ]
 
 
:If ''Cumulative'' is true, creates cumulative distribution function of t-distribution, otherwise creates pdf of t-distribution.
 
:If ''Cumulative'' is true, creates cumulative distribution function of t-distribution, otherwise creates pdf of t-distribution.
; TDistribution[ <Degrees of Freedom d>, <Variable Value v> ]: Calculates the value of cumulative distribution function of t-distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with t-distribution with ''d'' degrees of freedom.
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; TDistribution( <Degrees of Freedom>, <Variable Value> )
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: Calculates the value of cumulative distribution function of t-distribution at ''variable value v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with t-distribution with given degrees of freedom.
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:{{example|1=<code><nowiki>TDistribution(10, 0)</nowiki></code> yields ''0.5''.}}
 
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the t-distribution curve to the left of the given ''x''-coordinate).}}
 
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the t-distribution curve to the left of the given ''x''-coordinate).}}
 
==CAS Syntax==
 
==CAS Syntax==
;TDistribution[<Degrees of Freedom d>, <Variable Value v>]
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;TDistribution( <Degrees of Freedom>, <Variable Value> )
:Calculates the value of cumulative distribution function of T-distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with t-distribution with ''d'' degrees of freedom.
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:Calculates the value of cumulative distribution function of t-distribution at ''variable value v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with t-distribution with given degrees of freedom.
:{{example|1=<div><code><nowiki>TDistribution[10, 0]</nowiki></code> yields ''0.5''.</div>}}
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:{{example|1=<code><nowiki>TDistribution(10, 0)</nowiki></code> yields ''0.5''.}}

Latest revision as of 10:19, 30 July 2019


TDistribution( <Degrees of Freedom>, x )
Creates cumulative density function (cdf) of t-distribution with given degrees of freedom.
TDistribution( <Degrees of Freedom>, x, <Boolean Cumulative> )
If Cumulative is true, creates cumulative distribution function of t-distribution, otherwise creates pdf of t-distribution.
TDistribution( <Degrees of Freedom>, <Variable Value> )
Calculates the value of cumulative distribution function of t-distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with t-distribution with given degrees of freedom.
Example: TDistribution(10, 0) yields 0.5.
Note: Returns the probability for a given x-coordinate's value (or area under the t-distribution curve to the left of the given x-coordinate).

CAS Syntax

TDistribution( <Degrees of Freedom>, <Variable Value> )
Calculates the value of cumulative distribution function of t-distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with t-distribution with given degrees of freedom.
Example: TDistribution(10, 0) yields 0.5.
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