HyperGeometric Command
- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>)
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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> )
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Returns a bar graph of a Hypergeometric distribution when Cumulative = false. Returns the 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> )
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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
In the CAS View you can use
only the following syntax:
- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> )
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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.
Assume you select two balls out of ten balls, two of which are white, without putting any back.
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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 and -
HyperGeometric(10, 2, 2, 3, true)
yields 1, the probability of selecting three or less white balls.