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the integrand gives
:

Squaring the expression in the integral, the Cauchy-Schwarz inequality yields

:

The second bracketed factor is defined to be the Fisher Information, while the first bracketed factor is the mean-squared error (MSE) of the estimator . Since the estimator is unbiased, its MSE equals its variance. By rearranging, the inequality tells us that

:

In other words, the precision to which we

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