Theorem (8.6.6)

For any Random Variable $X$ and estimator $\hat{X}$, $$E\left[ (X-\hat{X})^{2} \right]\ge \frac{1}{2\pi e}e^{2h[X]}$$with equality if and only if $X$ is Gaussian and $\hat{X}=E_{}\left[ X \right]$.