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_posts/2024-11-18-Conditioning_joint_gaussian_on_sum.md

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@@ -20,14 +20,13 @@ The distribution of $X$ given the observation that the sum $S=s$ is given by
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$$X\mid S=s \sim \mathcal{N}\left(sv + A\mu, A\Sigma A^T\right),$$
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where $\mathbf{1}\in\mathbf{R}^n$ is the ones vector,
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where,
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$$v = \frac{1}{\mathbf{1}^T \Sigma \mathbf{1}}\Sigma\mathbf{1},$$
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and
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$$A=I-v\mathbf{1}^T.$$
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$$A=I-v\mathbf{1}^T,$$
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and $\mathbf{1}\in\mathbf{R}^n$ is the ones vector.
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### Proof
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