Difference between revisions of "Poisson 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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;Poisson( <Mean> )
;Poisson[ <Mean λ> ]
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:Returns a bar graph of a [[w:Poisson distribution|Poisson distribution]] with given mean ''λ''.
:Returns a bar graph of a [[w:Poisson distribution|Poisson distribution]] with given mean λ.
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;Poisson( <Mean>, <Boolean Cumulative> )
;Poisson[ <Mean λ>, <Boolean Cumulative> ]
 
 
:Returns a bar graph of a Poisson distribution when ''Cumulative = false''.  
 
:Returns a bar graph of a Poisson distribution when ''Cumulative = false''.  
:Returns a bar graph of a cumulative Poisson distribution when ''Cumulative = true''.
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:Returns a graph of a cumulative Poisson distribution when ''Cumulative = true''.
 
:The first parameter is same as above.
 
:The first parameter is same as above.
;Poisson[ <Mean λ>, <Variable Value v>, <Boolean Cumulative> ]
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;Poisson( <Mean>, <Variable Value v>, <Boolean Cumulative> )
:Let X be a Poisson random variable.
 
:Returns P( X = ''v'') when ''Cumulative'' = false. 
 
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
 
:First parameter is same as above.
 
==CAS Specific Syntax==
 
;Poisson[ <Mean λ>, <Variable Value v>, <Boolean Cumulative> ]
 
 
:Let X be a Poisson random variable.
 
:Let X be a Poisson random variable.
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
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:First parameter is same as above.
 
:First parameter is same as above.
  
:{{example|1=<div><code><nowiki>Poisson[3, 1, true]</nowiki></code> yields '' <math>\frac{4}{e³}</math>''.</div>}}
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:{{examples|1=<div>
:{{example|1=<div><code><nowiki>Poisson[3, 1, false]</nowiki></code> yields '' <math>\frac{3}{e³}</math>''.</div>}}
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:*<code><nowiki>Poisson(3, 1, true)</nowiki></code> yields ''0.2'' in the [[File:Menu view algebra.svg|link=|16px]] ''Algebra View'' and '' <math>\frac{4}{e³}</math> in the [[File:Menu view cas.svg|link=|16px]] ''CAS View''.
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:*<code><nowiki>Poisson(3, 1, false)</nowiki></code> yields ''0.15'' in the [[File:Menu view algebra.svg|link=|16px]] ''Algebra View'' and '' <math>\frac{3}{e³}</math>'' in the [[File:Menu view cas.svg|link=|16px]] ''CAS View''.</div>}}
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:{{Note|1=A simplified syntax is available to calculate P(''u'' ≤ X ≤ ''v''): e.g. <code>Poisson(1, 1..5)</code> yields ''0.63153'', that is the same as Poisson(1, {1, 2, 3, 4, 5}).}}

Latest revision as of 11:18, 11 October 2017


Poisson( <Mean> )
Returns a bar graph of a Poisson distribution with given mean λ.
Poisson( <Mean>, <Boolean Cumulative> )
Returns a bar graph of a Poisson distribution when Cumulative = false.
Returns a graph of a cumulative Poisson distribution when Cumulative = true.
The first parameter is same as above.
Poisson( <Mean>, <Variable Value v>, <Boolean Cumulative> )
Let X be a Poisson random variable.
Returns P( X = v) when Cumulative = false.
Returns P( X ≤ v) when Cumulative = true.
First parameter is same as above.
Examples:
  • Poisson(3, 1, true) yields 0.2 in the Menu view algebra.svg Algebra View and \frac{4}{e³} in the Menu view cas.svg CAS View.
  • Poisson(3, 1, false) yields 0.15 in the Menu view algebra.svg Algebra View and \frac{3}{e³} in the Menu view cas.svg CAS View.
Note: A simplified syntax is available to calculate P(u ≤ X ≤ v): e.g. Poisson(1, 1..5) yields 0.63153, that is the same as Poisson(1, {1, 2, 3, 4, 5}).
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