🎯 几何分布Geometric Distribution

使用说明与常见问题How-to & FAQ

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

首次成功均值 = 1/p（试验次数）。本地处理。可设置「成功概率 p」、「试验次数 k」。Mean trials until first success = 1/p. Processed locally. Settings: Success probability p, Trials k.

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

填写每次试验的成功概率 p 和试验次数 k，即可得到在第 k 次首次成功的概率等结果，以及平均所需次数 1/p。结果会随输入实时更新。Enter the success probability p and the trial number k to get the geometric-distribution results, such as the chance of the first success on trial k, and the mean number of trials, 1/p. The result updates as you type.

从 0？From 0?

本页 X=首次成功的试验序号（从 1 起）。X = trial number of first success (from 1).

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

例如在「几何分布」中填 成功概率 p = 0.2，试验次数 k = 3，结果区显示：均值（次数）：5；P(X=k)：0.128For example, entering Success probability p = 0.2, Trials k = 3 in the Geometric Distribution gives: Mean trials: 5; P(X=k): 0.128

哪些输入会被检查？Which inputs are validated?

「几何分布」会检查这些输入——「成功概率 p」：必须填写；「试验次数 k」：必须填写，须大于 0，须为整数；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 Geometric Distribution checks its inputs — "Success probability p": required; "Trials k": required, must be greater than 0, must be a whole number; 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?

「几何分布」的设置：「成功概率 p」默认 0.2；「试验次数 k」默认 3。每次生成结果都按当前设置处理。Settings in the Geometric Distribution — "Success probability p" default 0.2; "Trials k" default 3. The result always uses the current settings.

计算精度如何？How precise are the results?

「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 Geometric Distribution uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

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

「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 Geometric 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.