Chebyshev's Inequality
Revision as of 19:32, 13 March 2022 by Orange quail 9 (talk | contribs)
Chebyshev's inequality, named after Pafnuty Chebyshev, states that if and then the following inequality holds:
.
On the other hand, if and then: .
Proof
Chebyshev's inequality is a consequence of the Rearrangement inequality, which gives us that the sum is maximal when .
Now, by adding the inequalities:
we get the initial inequality.