diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex index f752f66..2469003 100644 --- a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex +++ b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex @@ -1 +1,9 @@ % P34 +\subsection{Stetigkeit der Verteilungsfunktion} +\shorttheorem[W. Punkt] Für Z.V $\cX$ und V.F $F_\cX$ gilt $\forall a \in \R$\\ +$\P[\cX = a] = F(a) - F(a-)$ mit $F(a-) := \underset{h\downarrow 0}{\lim} F(a - h)$. + +\begin{itemize}[label=$\bm{\rightarrow}$] + \item $F$ in $a$ n. stetig, dann ``Sprunghöhe''\\ $F(a) - F(a-) = \P[\cX = a]$ + \item $F$ stetig in $a$, dann $\P[\cX = a] = 0$ +\end{itemize} diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/01_almost-certain-events.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/01_almost-certain-events.tex new file mode 100644 index 0000000..78c1ba4 --- /dev/null +++ b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/01_almost-certain-events.tex @@ -0,0 +1,5 @@ +% P35 +\subsection{Fast sichere Ereignisse} +\shortdefinition $A \in \cF$ tritt \bi{fast sicher} (f.s.) ein, falls $\P[A] = 1$. + +\shortremark Für allg. Mengen: $A$ f.s., falls $\exists A' \subseteq A \divider \P[A'] = 1$ diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/02_discrete-rv.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/02_discrete-rv.tex new file mode 100644 index 0000000..d44a8dc --- /dev/null +++ b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/02_discrete-rv.tex @@ -0,0 +1 @@ +\subsection{Diskrete Zufallsvariablen} diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/03_examples-disc-rv.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/03_examples-disc-rv.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/04_cont-dist.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/04_cont-dist.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/05_examples-cont-rv.tex b/semester4/ps/ps-jh/parts/02_discrete-continuous-rv/05_examples-cont-rv.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index 116cd5a..ad7ca39 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 diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex index 7dfdb39..e783929 100644 --- a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex +++ b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex @@ -2,6 +2,8 @@ \PassOptionsToPackage{skip=0pt}{parskip} \input{~/projects/latex/janishutz-helpers.tex} + +\usepackage{bm} \usepackage{lmodern} \setFontType{sans} @@ -37,6 +39,11 @@ \newsectionNoPB \section{Diskrete und stetige ZV} \input{parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex} +\input{parts/02_discrete-continuous-rv/01_almost-certain-events.tex} +\input{parts/02_discrete-continuous-rv/02_discrete-rv.tex} +\input{parts/02_discrete-continuous-rv/03_examples-disc-rv.tex} +\input{parts/02_discrete-continuous-rv/04_cont-dist.tex} +\input{parts/02_discrete-continuous-rv/05_examples-cont-rv.tex} % \input{parts/02_discrete-continuous-rv/}