ChernoffBoundNote马尔可夫不等式切诺夫界非伯努利切诺夫界马尔可夫不等式设随机变量X的取值为非负数，马尔可夫不等式形式为：P(X≥ξ)≤E(X)ξP(X\ge\xi)\le\frac{E(X)}{\xi}P(X≥ξ)≤ξE(X)​proof.proof.proof.设非负随机变量XXX的概率密度函数为f(x)f(x)f(x)E(X)=∫0∞xf(x)dx=∫0ξxf(x)dx+∫ξ∞xf(x)dx≥∫ξ∞xf(x)dx≥∫ξ∞ξf(x)dx=ξP(X≥ξ)\begin{split}E(X)&=\int_{0}^{\infty}xf(x)dx\\&=\int_{0}^{\xi}xf