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[AMR] Fix errors pointed out to me

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janishutz
2026-08-09 08:30:17 +02:00
parent cc5f111813
commit a8b3bd7b20
24 changed files with 50 additions and 47 deletions
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electives/amr/parts/00_basics/00_probability.tex
+2 -2
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@@ -10,7 +10,7 @@ e.g. $\sum_{X} \P(X) = 1$ becomes $\int \P(x) \dx = 1$
\shortdefinition[Indep.] $x, y$ indep. iff $\P(\cX \cap \cY) = \P(\cX) \P(\cY)$
\shortdefinition[Cond. Indep.] iff $\P(\cX \cap \cY | \cZ) = \P(\cX | \cY) \P(\cY | \cZ)$
\shortdefinition[Cond. Indep.] iff $\P(\cX \cap \cY | \cZ) = \P(\cX | \cZ) \P(\cY | \cZ)$
\shortdefinition $\E[\vec{x}] = \int_{-\8}^{\8} \vec{x} \P(\vec{x}) \dx \vec{x}$, also for $\vec{x} = \vec{f(x)}$
@@ -19,6 +19,6 @@ e.g. $\sum_{X} \P(X) = 1$ becomes $\int \P(x) \dx = 1$
\shortdefinition[Gauss. Dist.] $\vec{x} \sim \cN(\vec{\mu}, \mat{\Sigma})$ ($\vec{\mu}$ mean, $\mat{\Sigma}$ cov.),\\
PDF: $f(\vec{x}) = \frac{1}{\sqrt{(2\pi)^k \det(\mat{\Sigma})}} \text{exp}\left( -\frac{1}{2}(\vec{x} - \vec{\mu})^\top \mat{\Sigma}^{-1} (\vec{x} - \vec{\mu}) \right)$
$\Sigma^{-1}$ for $\Sigma$ diagonal, inverse of diag els (e.g. $\sigma^{-1}$)
$\Sigma^{-1}$ for $\Sigma$ diagonal, inverse of diag els (e.g. $\sigma^{-2}$ for $\sigma^2$ on diags)
\hl{Always Normalize (i.e. sum of all probabilities is 1)}