📉 指数分布Exponential Distribution
均值 = 1/λ；P(X≤x) = 1-e^(-λx)。本地处理。可设置「λ」、「x」。Mean = 1/λ; P(X≤x) = 1-e^(-λx). Processed locally. Settings: λ, x.
使用说明与常见问题How-to & FAQ
「指数分布」是什么？What is the Exponential Distribution tool?
均值 = 1/λ；P(X≤x) = 1-e^(-λx)。本地处理。可设置「λ」、「x」。Mean = 1/λ; P(X≤x) = 1-e^(-λx). Processed locally. Settings: λ, x.
如何使用「指数分布」？How do I use the Exponential Distribution tool?
在「指数分布」中，填写「λ」、「x」等参数，结果会随输入实时计算并显示在下方。In the Exponential Distribution: Fill in "λ", "x"; results are recalculated instantly as you type.
λ 是什么意思？What is λ?
λ 是单位时间内事件发生的平均次数（发生率），例如每小时 2 次。均值（平均等待时间）= 1 ÷ λ，P(X ≤ x) = 1 − e^(−λx) 是在 x 时间内至少发生一次的概率。x 和 λ 要用同一时间单位。λ is the average number of events per unit time, for example 2 per hour. The mean waiting time is 1 ÷ λ, and P(X ≤ x) = 1 − e^(−λx) is the chance of at least one event within x. Use the same time unit for x and λ.
能举个计算实例吗？Can you show a worked example?
例如在「指数分布」中填 λ = 0.5，x = 2，结果区显示：均值：2；P(X≤x)：0.63212056For example, entering λ = 0.5, x = 2 in the Exponential Distribution gives: Mean: 2; P(X≤x): 0.63212056
哪些输入会被检查？Which inputs are validated?
「指数分布」会检查这些输入——「λ」：必须填写，须大于 0；「x」：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 Exponential Distribution checks its inputs — "λ": required, must be greater than 0; "x": 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?
「指数分布」的设置：「λ」默认 0.5；「x」默认 2。每次生成结果都按当前设置处理。Settings in the Exponential Distribution — "λ" default 0.5; "x" default 2. The result always uses the current settings.
计算精度如何？How precise are the results?
「指数分布」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 Exponential Distribution uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「指数分布」免费吗？需要注册吗？Is the Exponential Distribution free? Do I need an account?
「指数分布」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 Exponential 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.