If
 |
(1)
|
 |
(2)
|
then
 |
(3)
|
This is true for any distribution.
See also
Cauchy's Inequality,
Chebyshev
Inequality,
Hölder's Inequalities
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References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
p. 1092, 2000.Hardy, G. H.; Littlewood, J. E.; and Pólya,
G. Inequalities,
2nd ed. Cambridge, England: Cambridge University Press, pp. 43-44, 1988.Referenced
on Wolfram|Alpha
Chebyshev Sum Inequality
Cite this as:
Weisstein, Eric W. "Chebyshev Sum Inequality."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChebyshevSumInequality.html
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