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Let $ p, q $ be two probability densities on $ [0,1] $, strictly positive over $ (0,1) $. Let $ P $ be the cumulative function of $ p $, i.e., $ P(x) = \int_0^x p(x') \, \mathrm{d}x' $, $ x \in [0,1] $...

Given probability densities $f, g\in L^p(\mathbb{R}^3), \ \forall p\geq 1$, with the same first and second moments \begin{align} & \int_{\mathbb{R}^3} v f(v)\,dv = \int_{\mathbb{R}^3} v g(v)\,dv, \...