Date of this Version
The American Mathematical Monthly
For a positive random variable X, let μα(X) be the αth moment of X. Mark Brown proves that for positive and independent random variables X, Y, F(X + Y) ≥ F(X) + F(Y), where F (X) is the ratio μ-1 over μ-2. We prove this inequality and several generalizations by a method which can be used to prove the Schwarz inequality, but which is not widely appreciated.
Olkin, I., & Shepp, L. A. (2006). Several Colorful Inequalities. The American Mathematical Monthly, 113 (9), 817-822. http://dx.doi.org/10.2307/27642063
Date Posted: 27 November 2017
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