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# 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, which is unrelated.

Keywords:

variance, mean, deviation

Related:

MarkovsInequality, ChebyshevsInequality

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

60A99*no label found*

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