Gauss's Inequality

If a distribution has a single Mode at $\mu_0$ , then

$\begin{displaymath} P(\vert x-\mu_0\vert \geq \lambda\tau)\leq {4\over 9\lambda^2}, \end{displaymath}$

where

$\begin{displaymath} \tau^2\equiv\sigma^2+(\mu-\mu_0)^2. \end{displaymath}$