Abstract
In words: The expectation of the reciprocal of a nondegenerate positive random variable is greater than the reciprocal of its expectation. The reverse inequality holds if X assumes only negative values. This inequality is quite useful in statistical inference and stochastic processes and has been proven by using various approaches, such as Schwarz inequality [2], the concept of convexity [3], and others [1]. The present proof is somewhat simpler.
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