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Is variance larger if and only if tails are larger?

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Abstract

Suppose Vari and Fi are the variance and distribution function of two random variables with mean zero, i=1,2, and r=rr and rl are the largest and smallest points, respectively, where 0 Var2[left right double arrow]{F1(t)[greater-or-equal, slanted]F2(t) and 1-F1(s)[greater-or-equal, slanted]1-F2(s) for all s>rr and t

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