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fix: Typo
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YDX-2147483647 committed Sep 25, 2023
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2 changes: 1 addition & 1 deletion docs/course/statistical-digital-signal-processing.md
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Expand Up @@ -118,4 +118,4 @@ $$
\geq \frac{1}{- \expect \pdv[2]{\ln p}{\theta}}.
$$

Moreover, the two sides are equal if and only if $\qty(\hat\theta - \theta) \parallel \pdv{\theta}\ln p$ with respect to $\xi$. In other words, exists a function $\theta \mapsto \lambda$, such that $\pdv{\theta} \ln p = \lambda \qty(\hat\theta - \theta)$ (assuming $\hat\theta \not\equiv \theta$). Note that in this case, $1 = \expect\abs{\hat\theta - \theta}^2 \times \expect\abs{\lambda \qty(\hat\theta - \theta)}^2$, therefore $\expect\abs{\hat\theta - \theta}^2 = 1 / \abs{\lambda}$.
Moreover, the two sides are equal if and only if $\qty(\hat\theta - \theta) \parallel \pdv{\theta}\ln p$ with respect to $\xi$. In other words, there exists a function $\theta \mapsto \lambda$, such that $\pdv{\theta} \ln p = \lambda \qty(\hat\theta - \theta)$ (assuming $\hat\theta \not\equiv \theta$). Note that in this case, $1 = \expect\abs{\hat\theta - \theta}^2 \times \expect\abs{\lambda \qty(\hat\theta - \theta)}^2$, therefore $\expect\abs{\hat\theta - \theta}^2 = 1 / \abs{\lambda}$.

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