oldest votes up vote 1 down vote Consider an absolutely continuous distribution with location parameter $x_0$ and scale parameter $\sigma$. We consider two such distributions: normal $\mathcal{D}_1 = \mathcal{N}\left(x_0, \sigma\right)$, and continuous uniform $\mathcal{D}_2 = \mathcal{U}\left(x_0-\sqrt{3} \sigma, x_0+\sqrt{3} \sigma\right)$. Distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ have equal means and variances. Carrying out the