Prove that the square efficacy of the (t)-test equals (1,12, frac{1}{2}, 3 pi^{-2}), and 6 for the

Question:

Prove that the square efficacy of the $t$-test equals $1,12, \frac{1}{2}, 3 \pi^{-2}$, and 6 for the $\mathrm{N}(0,1), \operatorname{Uniform}\left(-\frac{1}{2}, \frac{1}{2}ight), \operatorname{LaPlace}(0,1)$, $\operatorname{Logistic}(0,1)$, and Triangular $(-1,1,0)$ densities, respectively.

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