🎯 期望值计算器Expected Value Calculator
输入离散随机变量的取值和对应概率，计算期望值 E(X)、方差和标准差；概率可填小数、百分数或分数，并检查概率之和是否为 1。Compute the expected value E(X), variance and standard deviation of a discrete random variable from its outcomes and probabilities — given as decimals, percentages or fractions — and check that they add up to 1.
使用说明与常见问题How-to & FAQ
「期望值计算器」是什么？What is the Expected Value Calculator tool?
输入离散随机变量的取值和对应概率，计算期望值 E(X)、方差和标准差；概率可填小数、百分数或分数，并检查概率之和是否为 1。Compute the expected value E(X), variance and standard deviation of a discrete random variable from its outcomes and probabilities — given as decimals, percentages or fractions — and check that they add up to 1.
如何使用「期望值计算器」？How do I use the Expected Value Calculator tool?
在「期望值计算器」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Expected Value Calculator: Fill in the fields above; results are recalculated instantly as you type.
期望值怎么计算？How is the expected value computed?
E(X) = Σ xᵢ·pᵢ，方差 Var(X) = Σ pᵢ·(xᵢ − E(X))²（与 E(X²) − E(X)² 相等，但数值更稳定），标准差是方差的平方根。E(X) = Σ xᵢ·pᵢ; Var(X) = Σ pᵢ·(xᵢ − E(X))² (equal to E(X²) − E(X)² but numerically more stable), and the standard deviation is its square root.
可以用来判断一个赌局值不值吗？Can I use it to judge a bet?
可以：把每种结果的净收益（输为负）和概率填进去，期望值为负说明长期平均会亏钱。Yes — enter each outcome's net gain (losses negative) with its probability; a negative expected value means you lose on average in the long run.
计算精度如何？How precise are the results?
「期望值计算器」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 Expected Value Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「期望值计算器」免费吗？需要注册吗？Is the Expected Value Calculator free? Do I need an account?
「期望值计算器」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 Expected Value Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.