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adding notes about fixing mathjax errors
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_posts/2018-02-15-conditional_distribution_for_jointly_gaussian_random_vectors.md

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_This is based on lectures from EE 278 Statistical Signal Processing at Stanford University_
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[Note: If the math notation is not rendering correctly, try following the steps described [here](https://physics.meta.stackexchange.com/a/14409) to set your MathJax renderer to "Common HTML".]
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### Background: Jointly Gaussian Random Vectors
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Jointly Gaussian random vectors are generalizations of the one-dimensional Gaussian (or normal) distribution to higher dimensions. Specifically, a vector is said to be jointly Gaussian (j-g) if each element of the vector is a linear combination of some number of i.i.d. standard, normal distributions (Gaussians with zero-mean and a variance of one) plus a bias term. In other words, if $X\in\mathbf{R}^n$ is a JG r.v., then

_posts/2024-11-18-Conditioning_joint_gaussian_on_sum.md

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_This is a follow-up to the [previous post]({{ "/conditional_distribution_for_jointly_gaussian_random_vectors/" | absolute_url}}) on conditioning a jointly Gaussian probability distribution on partial observations_
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[Note: If the math notation is not rendering correctly, try following the steps described [here](https://physics.meta.stackexchange.com/a/14409) to set your MathJax renderer to "Common HTML".]
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### Setting
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Let $X$ be a jointly Gaussian (j-g) random vector with mean $\mu\in\mathbf{R}^n$ and covariance matrix $\Sigma\in\mathbf{R}^{n\times n}$, such that $X\sim\mathcal{N}(\mu, \Sigma)$, and let $S$ be the sum of the entries of $X$. We are interested in the setting where we wish to update our belief about the distribuition of $X$ given our observation that the sum equals a specific value, $S=s$.

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