From ec39c30933637ab217e1cf12d5736d36c4caba2a Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sat, 21 Feb 2026 18:10:53 +0100 Subject: [PATCH] [PS] Start summarizing --- README.md | 2 +- .../ps/ps-jh/parts/00_basics/00_intro.tex | 1 - .../parts/00_basics/00_probability-space.tex | 23 ++++++++++++++++++ .../probability-and-statistics-cheatsheet.pdf | Bin 58074 -> 206998 bytes .../probability-and-statistics-cheatsheet.tex | 13 ++++++++-- 5 files changed, 35 insertions(+), 4 deletions(-) delete mode 100644 semester4/ps/ps-jh/parts/00_basics/00_intro.tex create mode 100644 semester4/ps/ps-jh/parts/00_basics/00_probability-space.tex diff --git a/README.md b/README.md index 5e2af17..e64c7ed 100644 --- a/README.md +++ b/README.md @@ -34,7 +34,7 @@ If you find mistakes, please open an issue or fix them yourself and open a PR. ### Semester 4 #### Probability & Statistics -- [Probability & Statistics Cheat-Sheet (TBD)](./semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf) Author: Janis Hutz +- [Probability & Statistics Cheat-Sheet (DE)](./semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf) Author: Janis Hutz - [Probability & Statistics Cheat-Sheet (TBD)](./semester4/ps/ps-rb/main.pdf) Author: Robin Bacher #### Other Courses - [Formal Methods & Functional Programming Summary (EN)](./semester4/fmfp/formal-methods-functional-programming-summary.pdf) diff --git a/semester4/ps/ps-jh/parts/00_basics/00_intro.tex b/semester4/ps/ps-jh/parts/00_basics/00_intro.tex deleted file mode 100644 index 2175d52..0000000 --- a/semester4/ps/ps-jh/parts/00_basics/00_intro.tex +++ /dev/null @@ -1 +0,0 @@ -\inline{definition} diff --git a/semester4/ps/ps-jh/parts/00_basics/00_probability-space.tex b/semester4/ps/ps-jh/parts/00_basics/00_probability-space.tex new file mode 100644 index 0000000..c04ece9 --- /dev/null +++ b/semester4/ps/ps-jh/parts/00_basics/00_probability-space.tex @@ -0,0 +1,23 @@ +\subsection{Wahrscheinlichkeitsräume} +\shortterm $\Omega$ \bi{Grundraum}, $\omega \in \Omega$ \bi{Elementarereignis} + +\shortdefinition[Sigma-Algebra] $\cF \subseteq \cP(\Omega)$ ist $\sigma$-Algebra, falls: +\begin{enumerate}[label=E\arabic*.] + \item $\Omega \subseteq \cF$ + \item $A \in \cF \Rightarrow A^C \in \cF$ ($A$ Ereignis $\Rightarrow$ nicht $A$ auch) + \item $A_1, A_2, \ldots \in \cF \Rightarrow \bigcup_{i = 1}^\infty A_i \in \cF$\\ + ($A_1, \ldots$ Ereignisse $\Rightarrow$ $A_1$ oder $A_2$ oder \dots ein Ereignis) +\end{enumerate} +\shortexample $\omega$-Algebren beim einmaligen Würfeln ($\Omega = \{ 1, 2, 3, 4, 5, 6 \}$) +\begin{itemize} + \item $\cF = \{ \emptyset, \{ 1, 2, 3, 4, 5, 6 \} \}$ + \item $\cF = \cP(\Omega)$, dabei $|\cF| = 64$ + \item $\cF = \{ \emptyset, \{ 1, 2 \}, \{ 3, 4, 5, 6 \}, \Omega \}$ +\end{itemize} +Keine $\omega$-Algebren sind bspw: +\begin{itemize} + \item $\cF = \{ \Omega \}$ (Komplementärereignis $\emptyset$ fehlt, E2 verletzt) + \item $\cF = \{ \emptyset, \{ 1, 2, 3 \}, \{ 4, 5, 6 \}, \{ 1 \}, \{ 2, 3, 4, 5, 6 \}, \Omega \}$\\ + (E3 verletzt, da bspw $\{ 4, 5, 6 \} \cup \{ 1 \} \notin \cF$) +\end{itemize} + diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index 6feb67b39595daaadca2eab9acc296140eb2ccd2..6c72d33f53833bb6333e1a622bf8a2b116a12675 100644 GIT binary patch literal 206998 zcmce-bFe7OvM0Q3+qP}nwr$(q%eL2Ewr!hx*|u$b=e(Ia-;J0T@#dd%E229J*%h6g zs9#oPlPZXa(K6DpLy^uc4zEJ75HJwf8(Bf|@IcY4csiI8&}+yWS(zHUK+!9^8oB&e zkC?raEfl?wki7?iHp5@^j12#E=|a)}J@Q{qF+$PH8oD@H{zbv~7sX%Wf8YP2P%?G4 zcXcv0btYi_t49fnUdGhU+{J=`k(JpMhpHZNg*#!as{{p;)GPN`L-y?t3{(g1#zb5|Au)y(8vB3EsV}bE+;rt_F zVEkL;{~0+jGW}yr{O6R3@gLJBroUzUpOFO9-$MUK)QO4tKgY!1PVk>$g6%)Y#NV3x z&oJ?y^G?kFn0I3S&v_^2f6O~E|L1Ii`5&_h=D&f!f5tm8|80K%h)uBmyCnVvX*ifU z{}-nDpCQeWmZUtkBudYRx{94GC7o5RRe^*sQ+&oD6GRb?1YE3TG;$WghD?#paqX=7 z(o$BZ?I{S^q=dlWg}S}|Bm)y^bQcB>H|`~_E6_w3MG?KvUD2$4|x}$fQAxq zoIRSRhjG*Ic`1ox=cuk+-0aV{&mm(NIC=0qFdT^JTOpwwEGr!;vZ($wZLyiV8Rmp? 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-\setup{Probability and Statistics} +\setupCheatSheet{Wahrscheinlichkeit und Statistik} +\loadGerman + +\setsubsectionnumbering{section} +\renewcommand{\examplenumbering}{off} \begin{document} \startDocument +\noverticalspacing -\input{parts/00_basics/00_intro.tex} +\section{Basics} +\input{parts/00_basics/00_probability-space.tex} \end{document}