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P/mean-mse.md
@@ -31,6 +31,7 @@ username: "salbalkus"
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$$ \label{eq:mean-mse}
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\mu = \operatorname*{arg\,min}_{a \in \mathbb{R}} E\left[ (X_i - a)^2 \right] \; .
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+$$
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**Proof:** Using the [linearity of expectation](/P/mean-lin), we can simplify the objective function:
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Setting the first derivative
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$$ \label{eq:dmse-da}
-\frac{d}{da} \left[ a^2 - 2a\mu + E(X_i^2) ] = 2a - 2\mu
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+\frac{d}{da} \left[ a^2 - 2a\mu + E(X_i^2) \right] = 2a - 2\mu
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$$
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to zero to perform a derivative test, we obtain:
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