Expectation bound from a polynomial tail: $\mathbb P\{X>t\}\le C t^{-m}$ with $m>1$ implies $\mathbb E X\le C^{1/m}\,\frac{m}{m-1}$

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Expectation bound from a polynomial tail: $\mathbb P\{X>t\}\le C t^{-m}$ with $m>1$ implies $\mathbb E X\le C^{1/m}\,\frac{m}{m-1}$ · Prove2Me