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Chebyshev's sum inequality

Another article treats Chebyshev's inequality in probability theory.

In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if

a_1 \geq a_2 \geq \cdots \geq a_n

and

b_1 \geq b_2 \geq \cdots \geq b_n,

then

n \sum_{k=1}^n a_kb_k \geq \left(\sum_{k=1}^n a_k\right)\left(\sum_{k=1}^n b_k\right).

Chebyshev's sum inequality follows from the rearrangement inequality.

Last updated: 05-28-2005 22:49:15
Science Fair Project Encyclopedia Contents Page
11-30-2008 18:11:33
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