Inequalities involving the mean and the standard deviation of nonnegative real numbers
© Oscar Rojo. 2006
Received: 22 December 2005
Accepted: 21 September 2006
Published: 8 November 2006
Let and be the mean and the standard deviation of the components of the vector , where with a positive integer. Here, we prove that if , then for . The equality holds if and only if the largest components of are equal. It follows that is a strictly increasing sequence converging to , the largest component of , except if the largest components of are equal. In this case, for all .
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