Binomial and Poisson probabilities: P(X = k), the cumulative P(X ≤ k), mean and variance, plus a small table around k. All mass functions are computed in log space (Lanczos ln-Γ), so B(10000, 0.5) is as comfortable as a coin flip.
The normal distribution has its own tool (with the interactive curve), and hypothesis testing its own — this page covers the two discrete workhorses.
Frequently asked questions
How large can n get?
Computation is log-space, so overflow is not the limit — your patience for a cumulative sum is. n up to a few thousand rounds instantly; the cumulative caps at a million terms.
When do I use Poisson instead of binomial?
Poisson approximates binomial when n is large and p is small (rule of thumb: n ≥ 20, p ≤ 0.05) — it models rare-event counts per interval.
中文说明
二项与泊松分布概率：P(X = k)、累积 P(X ≤ k)、均值与方差，外加 k 附近的小表格。质量函数全部在对数空间（Lanczos ln-Γ）计算，B(10000, 0.5) 和抛硬币一样轻松。
正态分布有专属工具（含交互曲线），假设检验也有专属页——本页补的是两个最常用的离散分布。
常见问题
n 最大能到多少？
对数空间计算，瓶颈不是溢出而是你等累积和的耐心。几千以内瞬间出结果；累积求和上限一百万项。
什么时候用泊松代替二项？
n 大 p 小时（经验法则：n ≥ 20 且 p ≤ 0.05）泊松近似二项——它刻画单位区间内的稀有事件计数。