Are there examples where an inequality about expected values of two random variables reverses when the expected value of logarithm is considered? More specifically, are there random variables $X,Y$ such that $\mathbb{E}{Y} > \mathbb{E}{X}$ but $\mathbb{E}{\log(Y)} < \mathbb{E}{\log( X) }$?
2026-04-11 11:08:27.1775905707
Examples where $\mathbb{E}{Y} > \mathbb{E}{X}$ but $\mathbb{E}{\log(Y)} < \mathbb{E}{\log(X)}$
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