📊 Beta 分布（均值/方差）Beta Distribution (mean/var)
均值 = α/(α+β)；方差 = αβ/((α+β)²(α+β+1))。本地处理。可设置「α」、「β」。Mean = α/(α+β); variance = αβ/((α+β)²(α+β+1)). Processed locally. Settings: α, β.
使用说明与常见问题How-to & FAQ
「Beta 分布（均值/方差）」是什么？What is the Beta Distribution (mean/var) tool?
均值 = α/(α+β)；方差 = αβ/((α+β)²(α+β+1))。本地处理。可设置「α」、「β」。Mean = α/(α+β); variance = αβ/((α+β)²(α+β+1)). Processed locally. Settings: α, β.
如何使用「Beta 分布（均值/方差）」？How do I use the Beta Distribution (mean/var) tool?
在「Beta 分布（均值/方差）」中，填写「α」、「β」等参数，结果会随输入实时计算并显示在下方。In the Beta Distribution (mean/var): Fill in "α", "β"; results are recalculated instantly as you type.
能算概率密度吗？Does it give the PDF?
不能，本页只给出均值 α ÷ (α + β) 和方差 αβ ÷ ((α + β)²(α + β + 1))。概率密度 f(x) = x^(α−1)(1 − x)^(β−1) ÷ B(α, β) 和累积概率需要统计软件或专门的计算器。No, only the mean α ÷ (α + β) and variance αβ ÷ ((α + β)²(α + β + 1)). The density f(x) = x^(α−1)(1 − x)^(β−1) ÷ B(α, β) and the CDF need statistics software or a dedicated tool.
能举个计算实例吗？Can you show a worked example?
例如在「Beta 分布（均值/方差）」中填 α = 2，β = 5，结果区显示：均值：0.28571429；方差：0.0255102041For example, entering α = 2, β = 5 in the Beta Distribution (mean/var) gives: Mean: 0.28571429; Variance: 0.0255102041
哪些输入会被检查？Which inputs are validated?
「Beta 分布（均值/方差）」会检查这些输入——「α」、「β」：必须填写，须大于 0；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 Beta Distribution (mean/var) checks its inputs — "α", "β": required, must be greater than 0; 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?
「Beta 分布（均值/方差）」的设置：「α」默认 2；「β」默认 5。每次生成结果都按当前设置处理。Settings in the Beta Distribution (mean/var) — "α" default 2; "β" default 5. The result always uses the current settings.
计算精度如何？How precise are the results?
「Beta 分布（均值/方差）」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 Beta Distribution (mean/var) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「Beta 分布（均值/方差）」免费吗？需要注册吗？Is the Beta Distribution (mean/var) free? Do I need an account?
「Beta 分布（均值/方差）」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 Beta Distribution (mean/var) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.