Difference between revisions of "BinomialDist Command"
From GeoGebra Manual
(This syntax also works in the CAS View) |
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)") |
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}} | ||
| − | ;BinomialDist | + | ;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]]. | ||
: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. | :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. | ||
| − | ;BinomialDist | + | ;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. | ||
:Returns a graph of a cumulative Binomial distribution when ''Cumulative'' = true. | :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. | ||
| − | ;BinomialDist | + | ;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. | :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. | ||
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==CAS Specific Syntax== | ==CAS Specific Syntax== | ||
In [[File:Menu view cas.svg|link=|16px]] [[CAS View]] only one syntax is allowed: | In [[File:Menu view cas.svg|link=|16px]] [[CAS View]] only one syntax is allowed: | ||
| − | ;BinomialDist | + | ;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. | :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. | ||
Revision as of 17:16, 7 October 2017
- 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.
- 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 
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: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.
