Prove that the square efficacy of the sign test equals (2 pi^{-1}, 4,1, frac{1}{4}), and 4 for

Question:

Prove that the square efficacy of the sign test equals $2 \pi^{-1}, 4,1, \frac{1}{4}$, and 4 for the $\mathrm{N}(0,1), \operatorname{Uniform}\left(-\frac{1}{2}, \frac{1}{2}ight)$, LaPlace $(0,1)$, Logistic $(0,1)$, and Triangular $(-1,1,0)$ densities, respectively.

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