Chebyshev’s inequality

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

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

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

Title	Chebyshev’s inequality
Canonical name	ChebyshevsInequality
Date of creation	2013-03-22 12:47:55
Last modified on	2013-03-22 12:47:55
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	6
Author	rspuzio (6075)
Entry type	Theorem
Classification	msc 60A99
Related topic	MarkovsInequality
Related topic	ChebyshevsInequality