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[PS] Fix more errors

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Janis Hutz
2026-02-28 20:47:26 +01:00
parent 0af2aeaa08
commit d02ddf44dc
3 changed files with 2 additions and 2 deletions
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2
semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex
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@@ -26,7 +26,7 @@ Sie sind nützlich für schwer zu berechnende W.
{\centering $\limni P[A_n] = \P\left[ \bigcup_{n = 1}^\8 A_n \right]$\\} {\centering $\limni P[A_n] = \P\left[ \bigcup_{n = 1}^\8 A_n \right]$\\}
und für $(B_n)$ mit $B_n \supseteq B_{n + 1}$ (mon. fallend) gilt:\\ und für $(B_n)$ mit $B_n \supseteq B_{n + 1}$ (mon. fallend) gilt:\\
$\limni P[B_n] = \P\left[ \bigcap_{n = 1}^\8 \right]$ $\limni P[B_n] = \P\left[ \bigcap_{n = 1}^\8 B_n \right]$
\shortremark Mit Monotonie: $\P[A_n] \leq \P[A_{n + 1}]$ und\\ \shortremark Mit Monotonie: $\P[A_n] \leq \P[A_{n + 1}]$ und\\
$\P[B_n] \geq \P[B_{n + 1}]$. Grenzwerte oben wohldefiniert. $\P[B_n] \geq \P[B_{n + 1}]$. Grenzwerte oben wohldefiniert.

2
semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex
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@@ -12,7 +12,7 @@
\forall A \in \cF \quad \P[A] = \sum_{i = 1}^{n} \P[A | B_i] \cdot \P[B_i] \forall A \in \cF \quad \P[A] = \sum_{i = 1}^{n} \P[A | B_i] \cdot \P[B_i]
\] \]
\shorttheorem[Bayes] $B_i$ wie oben, damm $\forall A$ mit $\P[A] > 0$: \shorttheorem[Bayes] $B_i$ wie oben, dann $\forall A$ mit $\P[A] > 0$:
\[ \[
\forall i = 1, \ldots, n \quad \P[B_i | A] = \frac{\P[A | B_i] \P[B_i]}{\sum_{j = 1}^{n} \P[A | B_j] \P[B_j]} \forall i = 1, \ldots, n \quad \P[B_i | A] = \frac{\P[A | B_i] \P[B_i]}{\sum_{j = 1}^{n} \P[A | B_j] \P[B_j]}
\] \]

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semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf
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