# Chebyshev’s inequality

Let $X\in\textbf{L}^{2}$ be a real-valued random variable with mean $\mu=\mathbb{E}[X]$ and variance $\sigma^{2}=\operatorname{Var}[X]$. Then for any standard of accuracy $t>0$,

 $\mathbb{P}\left\{\left|X-\mu\right|\geq t\right\}\leq\frac{\sigma^{2}}{t^{2}}.$

Note: There is another Chebyshev’s inequality (http://planetmath.org/ChebyshevsInequality), which is unrelated.

Title Chebyshev’s inequality ChebyshevsInequality 2013-03-22 12:47:55 2013-03-22 12:47:55 rspuzio (6075) rspuzio (6075) 6 rspuzio (6075) Theorem msc 60A99 MarkovsInequality ChebyshevsInequality