HyperGeometric 指令

本頁為官方文件，一般使用者無法修改，若有任何誤謬，請與官方聯絡。如欲編輯，請至本頁的開放版。

HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size> ]: 目前本頁中文說明尚未翻譯完成，請先連至英文說明。如果您有權限，請幫忙翻譯本頁的官方手冊。
HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Boolean Cumulative> ]: 目前本頁中文說明尚未翻譯完成，請先連至英文說明。如果您有權限，請幫忙翻譯本頁的官方手冊。
HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> ]: 目前本頁中文說明尚未翻譯完成，請先連至英文說明。如果您有權限，請幫忙翻譯本頁的官方手冊。

CAS 視窗

HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size> ]

目前本頁中文說明尚未翻譯完成，請先連至英文說明。如果您有權限，請幫忙翻譯本頁的官方手冊。

HyperGeometric[ <Population Size>, <Number of Successes>, <Sample Size>]

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.

In CAS View only one 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.

First three parameters are same as above.

範例：

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 tow or less white balls and
HyperGeometric[10, 2, 2, 3, true] yields 1, the probability of selecting three or less white balls.