Difference between revisions of "HyperGeometric Command"
From GeoGebra Manual
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==CAS Syntax== | ==CAS Syntax== | ||
− | In [[CAS View]] only | + | In the [[CAS View]] only the following syntax is allowed: |
;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value v>, <Boolean Cumulative> ]: | ;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value v>, <Boolean Cumulative> ]: | ||
:Let X be a Hypergeometric random variable. | :Let X be a Hypergeometric random variable. | ||
: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. | ||
− | : | + | :The first three parameters are the same as above. |
:{{example| 1=<div>Assume you select two balls out of ten balls, two of which are white, without putting any back. | :{{example| 1=<div>Assume you select two balls out of ten balls, two of which are white, without putting any back. | ||
:*<code><nowiki>HyperGeometric[10, 2, 2, 0, false]</nowiki></code> yields <math>\frac{28}{45}</math>, the probability of selecting zero white balls, | :*<code><nowiki>HyperGeometric[10, 2, 2, 0, false]</nowiki></code> yields <math>\frac{28}{45}</math>, the probability of selecting zero white balls, | ||
Line 34: | Line 34: | ||
:*<code><nowiki>HyperGeometric[10, 2, 2, 0, true]</nowiki></code> yields <math>\frac{28}{45}</math>, the probability of selecting zero (or less) white balls, | :*<code><nowiki>HyperGeometric[10, 2, 2, 0, true]</nowiki></code> yields <math>\frac{28}{45}</math>, the probability of selecting zero (or less) white balls, | ||
:*<code><nowiki>HyperGeometric[10, 2, 2, 1, true]</nowiki></code> yields <math>\frac{44}{45}</math>, the probability of selecting one or less white balls, | :*<code><nowiki>HyperGeometric[10, 2, 2, 1, true]</nowiki></code> yields <math>\frac{44}{45}</math>, the probability of selecting one or less white balls, | ||
− | :*<code><nowiki>HyperGeometric[10, 2, 2, 2, true]</nowiki></code> yields ''1'', the probability of selecting | + | :*<code><nowiki>HyperGeometric[10, 2, 2, 2, true]</nowiki></code> yields ''1'', the probability of selecting two or less white balls and |
:*<code><nowiki>HyperGeometric[10, 2, 2, 3, true]</nowiki></code> yields ''1'', the probability of selecting three or less white balls.</div>}} | :*<code><nowiki>HyperGeometric[10, 2, 2, 3, true]</nowiki></code> yields ''1'', the probability of selecting three or less white balls.</div>}} |
Revision as of 11:08, 14 September 2012
- HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>]
- Returns a bar graph of a Hypergeometric distribution.
- Parameters:
- Population size: number of balls in the urn
- Number of Successes: number of white balls in the urn
- Sample Size: number of balls drawn from the urn
The bar graph shows the probability function of the number of white balls in the sample.
- HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Boolean Cumulative> ]
- Returns a bar graph of a Hypergeometric distribution when Cumulative = false.
- Returns a bar graph of a cumulative Hypergeometric distribution when Cumulative = true.
- First three parameters are same as above.
- HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value v>, <Boolean Cumulative> ]
- Let X be a Hypergeometric random variable.
- Returns P( X = v) when Cumulative = false.
- Returns P( X ≤ v) when Cumulative = true.
- First three parameters are same as above.
CAS Syntax
In the CAS View only the following syntax is allowed:
- HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value v>, <Boolean Cumulative> ]
- Let X be a Hypergeometric random variable.
- Returns P( X = v) when Cumulative = false.
- Returns P( X ≤ v) when Cumulative = true.
- The first three parameters are the same as above.
- Example:Assume you select two balls out of ten balls, two of which are white, without putting any back.
HyperGeometric[10, 2, 2, 0, false]
yields \frac{28}{45}, the probability of selecting zero white balls,HyperGeometric[10, 2, 2, 1, false]
yields \frac{16}{45}, the probability of selecting one white ball,HyperGeometric[10, 2, 2, 2, false]
yields \frac{1}{45}, the probability of selecting both white balls,HyperGeometric[10, 2, 2, 3, false]
yields 0, the probability of selecting three white balls.HyperGeometric[10, 2, 2, 0, true]
yields \frac{28}{45}, the probability of selecting zero (or less) white balls,HyperGeometric[10, 2, 2, 1, true]
yields \frac{44}{45}, the probability of selecting one or less white balls,HyperGeometric[10, 2, 2, 2, true]
yields 1, the probability of selecting two or less white balls andHyperGeometric[10, 2, 2, 3, true]
yields 1, the probability of selecting three or less white balls.