Statistics 简明教程

Statistics - Hypergeometric Distribution

超几何随机变量是指超几何实验中产生的成功次数。超几何随机变量的概率分布称为 hypergeometric distribution 。

A hypergeometric random variable is the number of successes that result from a hypergeometric experiment. The probability distribution of a hypergeometric random variable is called a hypergeometric distribution.

超几何分布的定义和概率函数如下：

Hypergeometric distribution is defined and given by the following probability function:

Formula

其中——

Where −

  1. ${N}$ = items in the population

  2. ${k}$ = successes in the population.

  3. ${n}$ = items in the random sample drawn from that population.

  4. ${x}$ = successes in the random sample.

Example

Problem Statement:

Problem Statement:

假设我们从一副普通扑克牌中随机抽取 5 张牌，不允许放回。那么恰好抽到 2 张红心牌（即红桃或方块）的概率是多少？

Suppose we randomly select 5 cards without replacement from an ordinary deck of playing cards. What is the probability of getting exactly 2 red cards (i.e., hearts or diamonds)?

Solution:

Solution:

这是一个超几何实验，我们知道以下信息：

This is a hypergeometric experiment in which we know the following:

  1. N = 52; since there are 52 cards in a deck.

  2. k = 26; since there are 26 red cards in a deck.

  3. n = 5; since we randomly select 5 cards from the deck.

  4. x = 2; since 2 of the cards we select are red.

我们将这些值插入超几何公式，如下所示：

We plug these values into the hypergeometric formula as follows:

因此，随机选择 2 张红牌的概率为 0.32513。

Thus, the probability of randomly selecting 2 red cards is 0.32513.