Does anyone know a decent lower bound for the expected value of $E(\frac{x}{1+x})$ where $0<x<1$? Clearly $E(x/2)$ works, but I need something tighter. I want something in terms of $E(x)$ if possible. Using the inequality $\frac{x}{1+x} \geq x e^{-x}$ also didn't help, since I still need to take the expected value of that.
2026-04-02 18:36:17.1775154977
Decent lower bound on expected value
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