Difference between revisions of "BinomialDist 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}}
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{{command|probability}}
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;BinomialDist( <Number of Trials>, <Probability of Success> )
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;BinomialDist[ <Number of Trials>, <Probability of Success> ]
 
 
:Returns a bar graph of a [[w:Binomial distribution|Binomial distribution]].
 
:Returns a bar graph of a [[w:Binomial distribution|Binomial distribution]].
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:''Parameters:''
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:The parameter ''Number of Trials'' specifies the number of independent Bernoulli trials and the parameter ''Probability of Success'' specifies the probability of success in one trial.
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::''Number of Trials'': number of independent Bernoulli trials
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:{{Note|'''BinomialDist( <Number of Trials>, <Probability of Success>,<List of values>)''' is also available.}}
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::''Probability of Success'': probability of success in one trial
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;BinomialDist( <Number of Trials>, <Probability of Success>, <Boolean Cumulative> )
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;BinomialDist[ <Number of Trials>, <Probability of Success>, <Boolean Cumulative> ]
 
 
:Returns a bar graph of a Binomial distribution when ''Cumulative'' = false.
 
:Returns a bar graph of a Binomial distribution when ''Cumulative'' = false.
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:Returns a bar graph of a cumulative Binomial distribution when ''Cumulative'' = true.
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:Returns a graph of a cumulative Binomial distribution when ''Cumulative'' = true.
 
:First two parameters are same as above.
 
:First two parameters are same as above.
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;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value v>, <Boolean Cumulative> ]
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;BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
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:Let X be a Binomial random variable.
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:Let X be a Binomial random variable and let v be the variable value.
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
 
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
 
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
 
:First two parameters are same as above.
 
:First two parameters are same as above.
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:{{Note|1=A simplified syntax is available to calculate P(''u'' ≤ X ≤ ''v''): e.g. <code>BinomialDist(10, 0.2, 1..3)</code> yields ''0.77175'', that is the same as BinomialDist(10, 0.2, {1, 2, 3}). This syntax also works in the CAS View}}
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==CAS Specific Syntax==
 
==CAS Specific Syntax==
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In [[CAS View]] only one syntax is allowed:
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In [[File:Menu view cas.svg|link=|16px]] [[CAS View]] only one syntax is allowed:
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;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value v>, <Boolean Cumulative> ]
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;BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
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:Let X be a Binomial random variable.
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:Let X be a Binomial random variable and let v be the variable value.
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
 
:Returns P( X = ''v'') when ''Cumulative'' = false.   
 
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
 
:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
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:{{example| 1=<div>You can plot a graph with eg <code>f(x):=BinomialDist(100,x,36,true)-BinomialDist(100,x,23,true)</code></div>}}
 
:{{example| 1=<div>Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is <math>\frac{1}{10}</math>, hence the propability of transfering an arbitrary packet successfully is <math>\frac{9}{10}</math>.
 
:{{example| 1=<div>Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is <math>\frac{1}{10}</math>, hence the propability of transfering an arbitrary packet successfully is <math>\frac{9}{10}</math>.
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:*<code><nowiki>BinomialDist[3, 0.9, 0, false]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 0, false)</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 1, false]</nowiki></code> yields ''<math>\frac{27}{1000}</math>'', the probability of exactly one of three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 1, false)</nowiki></code> yields ''<math>\frac{27}{1000}</math>'', the probability of exactly one of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 2, false]</nowiki></code> yields ''<math>\frac{243}{1000}</math>'', the probability of exactly two of three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 2, false)</nowiki></code> yields ''<math>\frac{243}{1000}</math>'', the probability of exactly two of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 3, false]</nowiki></code> yields ''<math>\frac{729}{1000}</math>'', the probability of all three packets being transferred successfully.
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:*<code><nowiki>BinomialDist(3, 0.9, 3, false)</nowiki></code> yields ''<math>\frac{729}{1000}</math>'', the probability of all three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 0, true]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 0, true)</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 1, true]</nowiki></code> yields ''<math>\frac{7}{250}</math>'', the probability of at most one of three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 1, true)</nowiki></code> yields ''<math>\frac{7}{250}</math>'', the probability of at most one of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 2, true]</nowiki></code> yields ''<math>\frac{271}{1000}</math>'', the probability of at most two of three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 2, true)</nowiki></code> yields ''<math>\frac{271}{1000}</math>'', the probability of at most two of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 3, true]</nowiki></code> yields ''1'', the probability of at most three of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist(3, 0.9, 3, true)</nowiki></code> yields ''1'', the probability of at most three of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 4, false]</nowiki></code> yields ''0'', the probability of exactly four of three packets being transferred successfully,
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:*<code><nowiki>BinomialDist(3, 0.9, 4, false)</nowiki></code> yields ''0'', the probability of exactly four of three packets being transferred successfully.
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:*<code><nowiki>BinomialDist[3, 0.9, 4, true]</nowiki></code> yields ''1'', the probability of at most four of three packets being transferred successfully.</div>}}
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:*<code><nowiki>BinomialDist(3, 0.9, 4, true)</nowiki></code> yields ''1'', the probability of at most four of three packets being transferred successfully.</div>}}

Latest revision as of 01:01, 1 February 2024

BinomialDist

This article is about GeoGebra command.

Command Categories (All commands)


BinomialDist( <Number of Trials>, <Probability of Success> )
Returns a bar graph of a Binomial distribution.
The parameter Number of Trials specifies the number of independent Bernoulli trials and the parameter Probability of Success specifies the probability of success in one trial.
Note: BinomialDist( <Number of Trials>, <Probability of Success>,<List of values>) is also available.
BinomialDist( <Number of Trials>, <Probability of Success>, <Boolean Cumulative> )
Returns a bar graph of a Binomial distribution when Cumulative = false.
Returns a graph of a cumulative Binomial distribution when Cumulative = true.
First two parameters are same as above.
BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
Let X be a Binomial random variable and let v be the variable value.
Returns P( X = v) when Cumulative = false.
Returns P( X ≤ v) when Cumulative = true.
First two parameters are same as above.
Note: A simplified syntax is available to calculate P(u ≤ X ≤ v): e.g. BinomialDist(10, 0.2, 1..3) yields 0.77175, that is the same as BinomialDist(10, 0.2, {1, 2, 3}). This syntax also works in the CAS View

CAS Specific Syntax

In Menu view cas.svg CAS View only one syntax is allowed:

BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
Let X be a Binomial random variable and let v be the variable value.
Returns P( X = v) when Cumulative = false.
Returns P( X ≤ v) when Cumulative = true.
Example:
You can plot a graph with eg f(x):=BinomialDist(100,x,36,true)-BinomialDist(100,x,23,true)
Example:
Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is \frac{1}{10}, hence the propability of transfering an arbitrary packet successfully is \frac{9}{10}.
  • BinomialDist(3, 0.9, 0, false) yields \frac{1}{1000}, the probability of none of the three packets being transferred successfully.
  • BinomialDist(3, 0.9, 1, false) yields \frac{27}{1000}, the probability of exactly one of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 2, false) yields \frac{243}{1000}, the probability of exactly two of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 3, false) yields \frac{729}{1000}, the probability of all three packets being transferred successfully.
  • BinomialDist(3, 0.9, 0, true) yields \frac{1}{1000}, the probability of none of the three packets being transferred successfully.
  • BinomialDist(3, 0.9, 1, true) yields \frac{7}{250}, the probability of at most one of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 2, true) yields \frac{271}{1000}, the probability of at most two of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 3, true) yields 1, the probability of at most three of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 4, false) yields 0, the probability of exactly four of three packets being transferred successfully.
  • BinomialDist(3, 0.9, 4, true) yields 1, the probability of at most four of three packets being transferred successfully.
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