Difference between revisions of "HyperGeometric Command"
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: First three parameters are same as above. | : First three parameters are same as above. | ||
| − | ;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value | + | ;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> ] |
| − | : Let X be a Hypergeometric random variable. | + | : Let X be a Hypergeometric random variable and v 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. | ||
| Line 21: | Line 21: | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value | + | ;HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> ]: |
| − | :Let X be a Hypergeometric random variable. | + | :Let X be a Hypergeometric random variable and v 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. | ||
Revision as of 10:37, 22 March 2013
- 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>, <Boolean Cumulative> ]
- Let X be a Hypergeometric random variable and v the variable value.
- Returns P( X = v) when Cumulative = false.
- Returns P( X ≤ v) when Cumulative = true.
- First three parameters are same as above.
CAS Syntax
- HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> ]
- Let X be a Hypergeometric random variable and v the variable value.
- 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.
