🎰 超几何分布Hypergeometric Distribution

使用说明与常见问题How-to & FAQ

「超几何分布」是什么？What is the Hypergeometric Distribution tool?

P(X=k) = C(K,k)C(N-K,n-k)/C(N,n)。本地处理。可设置「总体 N」、「成功标签 K」、「抽取 n」、「抽中 k」。P(X=k) = C(K,k)C(N-K,n-k)/C(N,n). Processed locally. Settings: Population N, Success states K, Draws n, Observed k.

如何使用「超几何分布」？How do I use the Hypergeometric Distribution tool?

在「超几何分布」中，填写「总体 N」、「成功标签 K」、「抽取 n」、「抽中 k」等参数，结果会随输入实时计算并显示在下方。In the Hypergeometric Distribution: Fill in "Population N", "Success states K", "Draws n", "Observed k"; results are recalculated instantly as you type.

均值是多少？What is the mean?

超几何分布的均值是 n × K ÷ N（抽取次数 × 成功比例）。本页计算恰好抽到 k 个成功的概率 P(X = k) = C(K, k)·C(N − K, n − k) ÷ C(N, n)，即不放回抽样。The mean of the hypergeometric distribution is n × K ÷ N (draws × success fraction). This page computes the chance of exactly k successes, P(X = k) = C(K, k)·C(N − K, n − k) ÷ C(N, n), for sampling without replacement.

能举个计算实例吗？Can you show a worked example?

例如在「超几何分布」中填 总体 N = 50，成功标签 K = 10，抽取 n = 5，抽中 k = 2，结果区显示：P(X=k)：0.20983972For example, entering Population N = 50, Success states K = 10, Draws n = 5, Observed k = 2 in the Hypergeometric Distribution gives: P(X=k): 0.20983972

哪些输入会被检查？Which inputs are validated?

「超几何分布」会检查这些输入——「总体 N」、「抽取 n」：必须填写，须为整数；「成功标签 K」、「抽中 k」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Hypergeometric Distribution checks its inputs — "Population N", "Draws n": required, must be a whole number; "Success states K", "Observed k": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「超几何分布」的设置：「总体 N」默认 50；「成功标签 K」默认 10；「抽取 n」默认 5；「抽中 k」默认 2。每次生成结果都按当前设置处理。Settings in the Hypergeometric Distribution — "Population N" default 50; "Success states K" default 10; "Draws n" default 5; "Observed k" default 2. The result always uses the current settings.

计算精度如何？How precise are the results?

「超几何分布」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Hypergeometric Distribution uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「超几何分布」免费吗？需要注册吗？Is the Hypergeometric Distribution free? Do I need an account?

「超几何分布」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Hypergeometric Distribution is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.