diff --git a/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex b/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex index 67dd950..f8795eb 100644 --- a/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex +++ b/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex @@ -26,7 +26,7 @@ Sie sind nützlich für schwer zu berechnende W. {\centering $\limni P[A_n] = \P\left[ \bigcup_{n = 1}^\8 A_n \right]$\\} 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\\ $\P[B_n] \geq \P[B_{n + 1}]$. Grenzwerte oben wohldefiniert. diff --git a/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex b/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex index 9ec96e1..48bfbf3 100644 --- a/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex +++ b/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex @@ -12,7 +12,7 @@ \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 $\P[A] > 0$: \[ \forall i = 1, \ldots, n \quad \P[B_i | A] = \frac{\P[A | B_i] \P[B_i]}{\sum_{j = 1}^{n} \P[A | B_j] \P[B_j]} \] diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index efbd22a..32e7151 100644 Binary files a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf and b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf differ