HyperGeometric Command

HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>)

Returns a Hypergeometric distribution bar graph.

Parameters:

  • Population size: number of balls in an urn

  • Number of Successes: number of white balls in the urn

  • Sample Size: number of balls drawn from the urn

A random sample is repeatedly extracted from an urn, without replacement. HyperGeometric(100, 50, 5) generates a bar graph showing the probability distribution of the number of white balls in the sample.

HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Boolean Cumulative> )

When Cumulative = false returns a bar graph of a Hypergeometric distribution, otherwise it returns the graph of a cumulative Hypergeometric distribution function. 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. The first three parameters are same as above.

  • When Cumulative = false it returns P( X = v)

  • When Cumulative = true it returns P( X ≤ v)

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 and

  • HyperGeometric(10, 2, 2, 3, true) yields 1, the probability of selecting three or less white balls.

CAS Syntax

In the Menu view cas.svg CAS View you can use only the following 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. The first three parameters are the same as above.

  • When Cumulative = false it returns P( X = v)

  • When Cumulative = true it returns P( X ≤ v)