thomasba
/
vorlesungen
1
1
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Wahrscheinlichkeit

Browse Source
main
Thomas Ba. 14 years ago
parent 70dd79c259
commit a598afc776
7 changed files with 1605 additions and 12 deletions
Show Stats Download Patch File Download Diff File

24
Berechenbarkeits-KomplexTh/bilder/ds-vc.xml
Unescape View File

@ -1,7 +1,7 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221095307" modified="D:20111221113735"/>
<info created="D:20111221095307" modified="D:20111221131321"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
@ -244,15 +244,6 @@ h
64 768 l
128 704 l
</path>
<path stroke="black">
144 736 m
176 736 l
160 752 l
</path>
<path stroke="black">
176 736 m
160 720 l
</path>
<use name="mark/disk(sx)" pos="224 768" size="normal" stroke="red"/>
<use name="mark/disk(sx)" pos="224 704" size="normal" stroke="black"/>
<use name="mark/disk(sx)" pos="288 704" size="normal" stroke="red"/>
@ -286,5 +277,18 @@ h
</path>
<text transformations="translations" pos="64 688" stroke="black" type="label" width="57.617" height="6.808" depth="0" valign="baseline">Vortex Cover</text>
<text matrix="1 0 0 1 -7.38462 8.46154" transformations="translations" pos="320 752" stroke="black" type="label" width="10.628" height="7.49" depth="0" valign="baseline">$G&apos;$</text>
<path stroke="black">
144 736 m
176 736 l
176 736 l
</path>
<path stroke="black">
176 736 m
168 744 l
</path>
<path stroke="black">
168 728 m
176 736 l
</path>
</page>
</ipe>

172
Wahrscheinlichkeitstheorie_und_Statistik/Wahrscheinlichkeitstheorie_und_Statistik.tex
Unescape View File

@ -5,7 +5,7 @@
\usepackage{amssymb}
\usepackage{eurosym}
\usepackage{enumerate}
%\usepackage{multicol}
\usepackage{multicol}
%\usepackage{booktabs}
%\usepackage{pstricks}
%\usepackage{pst-node}
@ -26,7 +26,7 @@
{\end{mdef}\end{leftbar}}
%TEST ENDE
\usepackage{tabularx}
%\usepackage{graphicx}
\usepackage{graphicx}
\usepackage[usenames,dvipsnames]{color}
\usepackage{lastpage}
\usepackage{fancyhdr}
@ -1056,4 +1056,172 @@
Zugehörige Verteilungsfunktion \(F(x) = \phi(x) = \phi_{0,1}(x) \rightarrow\) hierfür: \underline{Tabellenwerte}
\end{mydef}
\includegraphics{bilder/1-6_dichtefunktion.eps}
Aus der Tabelle:\\
\bsp \(\phi(1.27) = 0.89796 \)\\
\( \phi(0) = \phi(0.00) = 0.5 \)\\
\( \phi(-1.27) = 1- \phi(1.27) = 1-0.89796 \)
Berechnung von \(\phi(-x)\):\\
\( \phi(-x) = 1 -\phi(x) \)
Wenn $X$ $N(0,1)$ verteilt ist, dann ist \( P(X\le b) = \phi(b), P(x\ge a) = 1-\phi(a), P(a\le x\le b) = \phi(b)-\phi(a), P(X=a)=0\)
Wenn $X$ $N(\mu,0)$ verteilt ist, dann ist…\\
\includegraphics{bilder/1-6_dichtefunktion_2.eps}\\
… \( \frac{X-\mu}{\rho} \) \( N(0,1)\) verteilt. Standardverteilung \(\to\) Tabelle Anwendbar.
\bsp Bauteile aus der Produktion $\to$ \underline{Länge des Bauteils} ist Normalverteilt. Mit \( \mu = 10cm\) (Normalverteilt), \( \sigma = 0.2cm \) (Streuung $\to$ Maß für die mittlere Abweichung von $\mu$)\\
$\to 10cm\pm 0.2cm$
Ausschuss liegt vor, wenn die Länge unter $9.5cm$ liegt.\\
Gesucht: Auschussanteil\\
\begin{align*}
\to P(X\le 9.5) &= P(\frac{x-\mu}{\sigma} \le \frac{0.9-\mu}{\sigma})\\
&= P(\underbrace{\frac{x-\mu}{\sigma}}_{\text{ist }N(0,1)\text{ verteilt}} \le \frac{9.5-10}{0.2})\\
&= P(\frac{x-\mu}{\sigma} \le -2.5) = \phi(-2.5)\\
&= 1-\phi(2.5) = 1-0.99379\\
&= 0.00621
\end{align*}
Wie viel \% der Bauteile nimmt uns ein Kunde ab, wenn er eine Länge zwischen $9.7$ und $10.25$ benötigt?
\begin{align*}
P(9.7\le X<10.25) &= P\left( \frac{9.7-\mu}{\sigma} \le \frac{x-\mu}{\sigma} < \frac{10.25-\mu}{\sigma}\right)\\
&= P\left(\frac{-0.3}{0.2}\le \frac{x-\mu}{\sigma}<\frac{0.25}{0.2}\right)\\
&= \phi(\frac{0.25}{0.2}) - \phi(\frac{-0.3}{0.2})\\
&= \phi(1.25) - \phi(-1.5) = \phi(1.25) - (1-\phi(1.5)) \\
&= 0.89435 - (1-0.93319)\\
&= 0.89435 - 0.06681\\
&= 0.82754 = \underline{\underline{82.754\%}}
\end{align*}
Berechne die Wahrscheinlichkeit, dass ein Bauteil länger als $10.7cm$ ist.
\begin{align*}
P(X>10.7) &= 1 - P(X<10.7)\\
&= 1-P(\frac{x-\mu}{\sigma} < \frac{10.7-\mu}{\sigma})\\
&= 1-P(\frac{x-\mu}{\sigma} < \frac{0.7}{0.2})\\
&= 1-P(\frac{x-\mu}{\sigma} < 3.5)\\
&= 1 - \phi(3.5) = 1-0.99977\\
&= 0.00023 = \underline{\underline{0.023\%}}
\end{align*}
\subsection{Schätzungen und Tests}
Test z.\,B. Liefert die Maschine im Mittel die geforderten $10cm$ Länge?\\
\(\to\) mit einer Stichprobe.
\subsubsection{Stichproben}
Stichprobenumfang $n$, Stichprobenwerte \(x_1,x_2,…,x_n\).\\
$\to$ arithmetisches Mittel (Durchschnitt)
\( \overline{x} = \frac1n * (x_1+x_2+…+x_n) = \frac1n \sum\limits_{i=1}^n x_i \)\\
\( \to\) Schätzung für $\mu$
Stichprobenvarianz
\begin{align*}
s_{\color{Orange}n}^2 &= \frac{1}{\color{Orange}n} * \left( (x_1-\overline{x})^2 + (x_2-\overline{x})^2+ … + (x_n-\overline{x})^2 \right) \\
&= \frac1n * \left( x_1^2 + x_2^2 + … + x_n^2 \right) - \overline{x}^2\\
s^2 = s_{\color{Orange}n-1}^2 &= \frac{1}{\color{Orange}n-1} + \left( (x_1 - \overline{x})^2 + (x_2 - \overline{x})^2 + … + (x_n - \overline{x})^2 \right)\\
&= \frac{1}{n-1} * (x_1^2 + … + x_n^2) - \frac{n}{n-1} * \overline{x}^2
\end{align*}
% Datum: 2011-12-21
\begin{align*}
\overline{x} &= \frac1n * \left( x_1+x_2+…+x_n \right) & \textcolor{Orange}{\to \text{ Schätzwert für }\mu}\\
s^2 = s_{n-1}^2 &= \frac{1}{n-1} \left( x_1^2 + x_2^2 + … + x_n^2 \right) - \frac{n}{n-1}*\overline{x}^2\\
s = s_{n-1} &= \sqrt{s_{n-1}^2} & \textcolor{Orange}{\to \text{ Schätzwert für }\sigma}
\end{align*}
\bsp Stichprobe mit 100 Bauteilen aus der Produktion\\
$\to$ gemessene Lösungen: 50 mal 10cm, 20 mal 10.1cm, 10 mal 10.2cm, 20 mal 9.9cm.
\begin{align*}
\overline{x} &= \frac{1}{100} * (50*10 + 20*10.1 + 10*10.2 + 20*9.9)\\
&= 10.02 \\
s^2 &= \frac{1}{100} * (50*10^2 + 20*10.1^2 + 10*10.2^2 + 20*9.9^2) - \frac{100}{99} * 10.02^2\\
&= \frac{19}{2475} \approx 0.007677\\
s &= \sqrt{\frac{19}{2475}} = \frac{\sqrt{209}}{165} \approx 0.08762
\end{align*}
\textcolor{Green}{Maß für die Streuung: $0.0876cm$\\($\to\ 10.02\pm 0.08762cm$)}
\subsubsection{Zentraler Grenzwertsatz}\label{sec:zentraler_grenzwertsatz}
Wenn die Zufallsvariablen $X_i\ , i=1,2,3,…$ unabhängig ($X_1,X_2$ sind unabhängig, wenn $P(X_1=a \land X_2=b) = P(X_1=a)*P(X_2=b)$) und identisch Verteilt (alle $X_i$ besitzen die gleiche Verteilungsfunktion) sind mit Erwartungswert \(\mu=E(X_i)\) und Varianz \(\sigma^2 = Var(X_i) \), dann gilt für die Zufallsvariable \(\overline{X}=\frac1n*\left(X_1+X_2+…+X_n\right)\):\\
\( \frac{\overline{X}-\mu}{\sigma} * \sqrt{n} \) ist für große $n$ näherungsweise $N(0,1)$ verteilt.\\
(und: Konvergenz für \(n\to\infty\))
\includegraphics{bilder/1-6_dichtefunktion_3.eps}
\subsubsection{Tests (Erwartungswerttests)}
\underline{Nullhypothese} $\to$ soll getestet werden beim Erwartungswerttest:\\
\(H_0: \mu = \mu_0 \) z.\,B. Sollwert der Bauteillängen\\
\(\to\) Zweiseitiger Test\\
oder \(H_0: \mu\le\mu_0\) oder \(H_0: \mu\ge\mu_0 \)\\
\(\to\) Einseitige Tests
Testgröße \(T=\frac{\overline{X}-\mu_0}{\sigma} * \sqrt{n} \)\\
i\(\to\) ist für große $n$ näherungsweise $N(0,1)$ verteilt (siehe \ref{sec:zentraler_grenzwertsatz}) wenn $H_0$ stimmt.
\includegraphics{bilder/1-6_dichtefunktion_4.eps}
Man muss sich eine \underline{Irrtumswahrscheinlichkeit} $\alpha$ vorgeben (z.\,B. \(\alpha = 1\%, 2\% \text{ oder } 5\%\))\\
Testentscheidung: $H_0$ wird \( \begin{cases} \text{angenommen}, &\text{wenn } -c\le T\le c\\ \text{abgelehnt}, &\text{wenn } T> c \text{ oder } T< -c \end{cases} \)
Bestimmung von $c$:
\begin{align*}
\phi(c) &= 1-\frac{\alpha}{2}\\
c &= \phi^{-1}(1-\frac{\alpha}{2}) & \text{in der Tabelle: rückwärts}
\end{align*}
\underline{Vorgehensweise beim Test}\\
\begin{itemize}
\item aus den vorgegebenen $\alpha$ wird $c$ bestimmt: \(\phi(c) = 1-\frac{\alpha}{2} \to \)\underline{$c$ aus der Tabelle}
\item in der Stichprobe wird $\overline{x}$ (und evtl. $s$) bestimmt\\
\(\to\) Testgröße \(T=\frac{\overline{x}-\mu_0}{\sigma} * \sqrt{n} \) ($\sigma$ kann durch $s$ angenähert werden)
\item Testentscheidung: $H_0$ wird \( \begin{cases} \text{angenommen}, &\text{wenn } -c\le T\le c\\ \text{abgelehnt}, &\text{wenn } T> c \text{ oder } T< -c \end{cases} \)
\end{itemize}
\bsp aus \ref{sec:zentraler_grenzwertsatz}:\\
zusätzliche Angaben: Sollwert: $10cm$ ($\mu_0$); Irrtumswahrscheinlichkeit: $2\%$ ($\alpha$)
\begin{multicols}{2}
\begin{align*}
c &= \phi^{-1}\left(1-\frac{\alpha}{2}\right)\\
&= \phi^{-1}\left( 1- \frac{0.02}{2}\right)\\
&= \phi^{-1}( 1- 0.01 )\\
&= \phi^{-1}( 0.99) \\
&= 2.33
\end{align*}
\begin{align*}
T &= \frac{10.02-10}{0.08762} * \sqrt{100}\\
&= \frac{0.02}{0.08762} * 10 = \frac{0.2}{0.08762}\\
&= 2.28258
\end{align*}
\end{multicols}
Testentscheidung: \(\underbrace{-c}_{-2.33}\le \underbrace{T}_{2.283}\le \underbrace{c}_{2.33}\)\\
\(\Rightarrow H_0\) annehmen, d.\,h. es spricht nichts dagegen, dass die Maschine im Mittel den Sollwert produziert.\\
\textcolor{Orange}{Nullhypothese: $\mu=\mu_0=10$}
Bisher: zweiseitiger Test: \(H_0: \mu=\mu0\)\\
Jetzt: \underline{einseitige} Tests:\\
\(H_0: \mu\le\mu_0\) (vorgegebener Maximalwert)
\includegraphics{bilder/1-6_dichtefunktion_5.eps}
Testentscheidung:\\
$H_0$ wird \(\begin{cases}\text{angenommen},&\text{wenn } T\le c\\\text{abgelehnt},&\text{wenn }T>c\end{cases}\)
im \bsp wenn die Bauteile \underline{maximal $10cm$} lang sein dürfen.\\
\(\to H_0: \mu \le \underbrace{\mu_0}_{=10} \)
\(T=2.283\) (wie beim zweiseitigen Test)\\
für $\alpha = 2\%$:
\( \phi(c) = 1-\alpha = 1-0.02 = 0.98 \Rightarrow c=2.06 \)
Testentscheidung:\\
\( \underbrace{T}_{2.283} > \underbrace{c}_{2.06} \to H_0\) ablehnen $\to$ die Maschine liefert zu lange Teile (wahrscheinlich)
\end{document}

296
Wahrscheinlichkeitstheorie_und_Statistik/bilder/1-6_dichtefunktion.xml
Unescape View File

@ -0,0 +1,296 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221134146" modified="D:20111221135246"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<pen name="heavier" value="0.8"/>
<pen name="fat" value="1.2"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="red" value="1 0 0"/>
<color name="green" value="0 1 0"/>
<color name="blue" value="0 0 1"/>
<color name="yellow" value="1 1 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="gray" value="0.745"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="navy" value="0 0 0.502"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<textsize name="large" value="\large"/>
<textsize name="Large" value="\Large"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="huge" value="\huge"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="small" value="\small"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<anglesize name="90 deg" value="90"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="22.5 deg" value="22.5"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<page>
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<path layer="alpha" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path matrix="-1 0 0 1 256 0" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path stroke="black" arrow="normal/normal">
128 700 m
128 768 l
</path>
<text matrix="1 0 0 1 -8 0" transformations="translations" pos="124 692" stroke="red" type="label" width="24.268" height="6.428" depth="1.93" valign="baseline">$\mu = 0$</text>
<path stroke="black" arrow="normal/normal">
56 704 m
200 704 l
</path>
<text transformations="translations" pos="144 740" stroke="red" type="label" width="79.411" height="7.473" depth="2.49" valign="baseline">$N(0,1)$ Verteilung</text>
<text transformations="translations" pos="144 752" stroke="red" type="label" width="81.805" height="6.918" depth="0" valign="baseline">Dichtefunktion der</text>
<path matrix="1 0 0 1 0 -8" stroke="black" arrow="normal/normal">
56 624 m
200 624 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="black" arrow="normal/normal">
128 620 m
128 688 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="black" dash="dotted">
128 656 m
192 656 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="red">
80 628 m
112 628
128 640
144 652
176 652
176 652 s
</path>
<use matrix="1 0 0 1 0 -8" name="mark/disk(sx)" pos="128 640" size="normal" stroke="black"/>
<text matrix="1 0 0 1 -4 -8" transformations="translations" pos="124 652" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">$1$</text>
<text matrix="1 0 0 1 0 -8" transformations="translations" pos="136 636" stroke="black" type="label" width="6.362" height="8.422" depth="3.43" valign="baseline">$\frac 1 2$</text>
<text matrix="1 0 0 1 -8 -20" transformations="translations" pos="64 656" stroke="black" type="label" width="50.946" height="6.23" depth="1.74" valign="baseline" size="small">Wendepunkt</text>
<text matrix="1 0 0 1 0 4" transformations="translations" pos="144 672" stroke="red" type="label" width="85.319" height="6.926" depth="1.93" valign="baseline">Verteilungsfunktion</text>
<text transformations="translations" pos="144 664" stroke="red" type="label" width="76.204" height="7.473" depth="2.49" valign="baseline">$\phi(x) = P(X\le x)$</text>
<text matrix="1 0 0 1 0 -4" transformations="translations" pos="144 656" stroke="red" type="label" width="96.596" height="7.473" depth="2.49" valign="baseline">der $N(0,1)$ Verteilung</text>
<path stroke="black" arrow="normal/normal">
108 640 m
124 636 l
</path>
</page>
</ipe>

256
Wahrscheinlichkeitstheorie_und_Statistik/bilder/1-6_dichtefunktion_2.xml
Unescape View File

@ -0,0 +1,256 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221140527" modified="D:20111221140540"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<pen name="heavier" value="0.8"/>
<pen name="fat" value="1.2"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="red" value="1 0 0"/>
<color name="green" value="0 1 0"/>
<color name="blue" value="0 0 1"/>
<color name="yellow" value="1 1 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="gray" value="0.745"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="navy" value="0 0 0.502"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<textsize name="large" value="\large"/>
<textsize name="Large" value="\Large"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="huge" value="\huge"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="small" value="\small"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<anglesize name="90 deg" value="90"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="22.5 deg" value="22.5"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<page>
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<path layer="alpha" stroke="red">
96 712 m
128 712
144 736
160 760
176 736
192 712
208 712
208 712 s
</path>
<path stroke="black" arrow="normal/normal">
88 704 m
216 704 l
</path>
<use name="mark/disk(sx)" pos="160 704" size="normal" stroke="black"/>
<text transformations="translations" pos="160 696" stroke="black" type="label" width="6.003" height="4.297" depth="1.93" valign="baseline">$\mu$</text>
<path stroke="black" arrow="normal/normal">
128 696 m
128 768 l
</path>
</page>
</ipe>

287
Wahrscheinlichkeitstheorie_und_Statistik/bilder/1-6_dichtefunktion_3.xml
Unescape View File

@ -0,0 +1,287 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221134146" modified="D:20111221150651"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<pen name="heavier" value="0.8"/>
<pen name="fat" value="1.2"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="red" value="1 0 0"/>
<color name="green" value="0 1 0"/>
<color name="blue" value="0 0 1"/>
<color name="yellow" value="1 1 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="gray" value="0.745"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="navy" value="0 0 0.502"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<textsize name="large" value="\large"/>
<textsize name="Large" value="\Large"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="huge" value="\huge"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="small" value="\small"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<anglesize name="90 deg" value="90"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="22.5 deg" value="22.5"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<page>
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<path layer="alpha" matrix="1 0 0 1 0 -8" stroke="black" arrow="normal/normal">
56 624 m
200 624 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="black" arrow="normal/normal">
128 620 m
128 688 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="black" dash="dotted">
128 656 m
192 656 l
</path>
<path matrix="1 0 0 1 0 -8" stroke="red">
80 628 m
112 628
128 640
144 652
176 652
176 652 s
</path>
<use matrix="1 0 0 1 0 -8" name="mark/disk(sx)" pos="128 640" size="normal" stroke="black"/>
<text matrix="1 0 0 1 -4 -8" transformations="translations" pos="124 652" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">$1$</text>
<path stroke="yellow">
80 620 m
112 620 l
112 624 l
144 624 l
144 632 l
160 632 l
160 644 l
176 644 l
176 644 l
</path>
<path stroke="orange">
80 620 m
104 620 l
104 624 l
120 624 l
120 628 l
128 628 l
128 632 l
132 632 l
132 636 l
136 636 l
136 640 l
144 640 l
144 644 l
176 644 l
</path>
<text transformations="translations" pos="136 668" stroke="yellow" type="label" width="61.273" height="6.918" depth="0" valign="baseline">Fuer kleines $n$</text>
<text transformations="translations" pos="136 656" stroke="orange" type="label" width="62.241" height="6.815" depth="1.93" valign="baseline">Fuer grosses $n$</text>
</page>
</ipe>

280
Wahrscheinlichkeitstheorie_und_Statistik/bilder/1-6_dichtefunktion_4.xml
Unescape View File

@ -0,0 +1,280 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221154715" modified="D:20111221154746"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<pen name="heavier" value="0.8"/>
<pen name="fat" value="1.2"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="red" value="1 0 0"/>
<color name="green" value="0 1 0"/>
<color name="blue" value="0 0 1"/>
<color name="yellow" value="1 1 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="gray" value="0.745"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="navy" value="0 0 0.502"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<textsize name="large" value="\large"/>
<textsize name="Large" value="\Large"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="huge" value="\huge"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="small" value="\small"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<anglesize name="90 deg" value="90"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="22.5 deg" value="22.5"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<page>
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<path layer="alpha" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path matrix="-1 0 0 1 256 0" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path stroke="black" arrow="normal/normal">
128 700 m
128 768 l
</path>
<path stroke="black" arrow="normal/normal">
56 704 m
200 704 l
</path>
<path fill="yellow" tiling="rising">
64 708 m
80.2511 708.082 l
80.3468 704 l
64.0993 704 l
64.0993 708 l
64 708 l
</path>
<path fill="yellow" tiling="rising">
192 708 m
176.003 708.077 l
176.111 704 l
192.168 704 l
192 708 l
192 708 l
</path>
<text transformations="translations" pos="80 696" stroke="yellow" type="label" width="12.06" height="5.812" depth="0.83" valign="baseline">$-c$</text>
<text transformations="translations" pos="176 696" stroke="yellow" type="label" width="4.311" height="4.289" depth="0" valign="baseline">$c$</text>
</page>
</ipe>

302
Wahrscheinlichkeitstheorie_und_Statistik/bilder/1-6_dichtefunktion_5.xml
Unescape View File

@ -0,0 +1,302 @@
<?xml version="1.0"?>
<!DOCTYPE ipe SYSTEM "ipe.dtd">
<ipe version="70005" creator="Ipe 7.1.1">
<info created="D:20111221170547" modified="D:20111221170547"/>
<ipestyle name="basic">
<symbol name="arrow/arc(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/farc(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="mark/circle(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</symbol>
<symbol name="mark/disk(sx)" transformations="translations">
<path fill="sym-stroke">
0.6 0 0 0.6 0 0 e
</path>
</symbol>
<symbol name="mark/fdisk(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
0.5 0 0 0.5 0 0 e
</path>
<path fill="sym-stroke" fillrule="eofill">
0.6 0 0 0.6 0 0 e
0.4 0 0 0.4 0 0 e
</path>
</group>
</symbol>
<symbol name="mark/box(sx)" transformations="translations">
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</symbol>
<symbol name="mark/square(sx)" transformations="translations">
<path fill="sym-stroke">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
</path>
</symbol>
<symbol name="mark/fsquare(sfx)" transformations="translations">
<group>
<path fill="sym-fill">
-0.5 -0.5 m
0.5 -0.5 l
0.5 0.5 l
-0.5 0.5 l
h
</path>
<path fill="sym-stroke" fillrule="eofill">
-0.6 -0.6 m
0.6 -0.6 l
0.6 0.6 l
-0.6 0.6 l
h
-0.4 -0.4 m
0.4 -0.4 l
0.4 0.4 l
-0.4 0.4 l
h
</path>
</group>
</symbol>
<symbol name="mark/cross(sx)" transformations="translations">
<group>
<path fill="sym-stroke">
-0.43 -0.57 m
0.57 0.43 l
0.43 0.57 l
-0.57 -0.43 l
h
</path>
<path fill="sym-stroke">
-0.43 0.57 m
0.57 -0.43 l
0.43 -0.57 l
-0.57 0.43 l
h
</path>
</group>
</symbol>
<symbol name="arrow/fnormal(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/pointed(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/fpointed(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-0.8 0 l
-1 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/linear(spx)">
<path stroke="sym-stroke" pen="sym-pen">
-1 0.333 m
0 0 l
-1 -0.333 l
</path>
</symbol>
<symbol name="arrow/fdouble(spx)">
<path stroke="sym-stroke" fill="white" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<symbol name="arrow/double(spx)">
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
0 0 m
-1 0.333 l
-1 -0.333 l
h
-1 0 m
-2 0.333 l
-2 -0.333 l
h
</path>
</symbol>
<pen name="heavier" value="0.8"/>
<pen name="fat" value="1.2"/>
<pen name="ultrafat" value="2"/>
<symbolsize name="large" value="5"/>
<symbolsize name="small" value="2"/>
<symbolsize name="tiny" value="1.1"/>
<arrowsize name="large" value="10"/>
<arrowsize name="small" value="5"/>
<arrowsize name="tiny" value="3"/>
<color name="red" value="1 0 0"/>
<color name="green" value="0 1 0"/>
<color name="blue" value="0 0 1"/>
<color name="yellow" value="1 1 0"/>
<color name="orange" value="1 0.647 0"/>
<color name="gold" value="1 0.843 0"/>
<color name="purple" value="0.627 0.125 0.941"/>
<color name="gray" value="0.745"/>
<color name="brown" value="0.647 0.165 0.165"/>
<color name="navy" value="0 0 0.502"/>
<color name="pink" value="1 0.753 0.796"/>
<color name="seagreen" value="0.18 0.545 0.341"/>
<color name="turquoise" value="0.251 0.878 0.816"/>
<color name="violet" value="0.933 0.51 0.933"/>
<color name="darkblue" value="0 0 0.545"/>
<color name="darkcyan" value="0 0.545 0.545"/>
<color name="darkgray" value="0.663"/>
<color name="darkgreen" value="0 0.392 0"/>
<color name="darkmagenta" value="0.545 0 0.545"/>
<color name="darkorange" value="1 0.549 0"/>
<color name="darkred" value="0.545 0 0"/>
<color name="lightblue" value="0.678 0.847 0.902"/>
<color name="lightcyan" value="0.878 1 1"/>
<color name="lightgray" value="0.827"/>
<color name="lightgreen" value="0.565 0.933 0.565"/>
<color name="lightyellow" value="1 1 0.878"/>
<dashstyle name="dashed" value="[4] 0"/>
<dashstyle name="dotted" value="[1 3] 0"/>
<dashstyle name="dash dotted" value="[4 2 1 2] 0"/>
<dashstyle name="dash dot dotted" value="[4 2 1 2 1 2] 0"/>
<textsize name="large" value="\large"/>
<textsize name="Large" value="\Large"/>
<textsize name="LARGE" value="\LARGE"/>
<textsize name="huge" value="\huge"/>
<textsize name="Huge" value="\Huge"/>
<textsize name="small" value="\small"/>
<textsize name="footnote" value="\footnotesize"/>
<textsize name="tiny" value="\tiny"/>
<textstyle name="center" begin="\begin{center}" end="\end{center}"/>
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
<gridsize name="4 pts" value="4"/>
<gridsize name="8 pts (~3 mm)" value="8"/>
<gridsize name="16 pts (~6 mm)" value="16"/>
<gridsize name="32 pts (~12 mm)" value="32"/>
<gridsize name="10 pts (~3.5 mm)" value="10"/>
<gridsize name="20 pts (~7 mm)" value="20"/>
<gridsize name="14 pts (~5 mm)" value="14"/>
<gridsize name="28 pts (~10 mm)" value="28"/>
<gridsize name="56 pts (~20 mm)" value="56"/>
<anglesize name="90 deg" value="90"/>
<anglesize name="60 deg" value="60"/>
<anglesize name="45 deg" value="45"/>
<anglesize name="30 deg" value="30"/>
<anglesize name="22.5 deg" value="22.5"/>
<tiling name="falling" angle="-60" step="4" width="1"/>
<tiling name="rising" angle="30" step="4" width="1"/>
</ipestyle>
<page>
<layer name="alpha"/>
<view layers="alpha" active="alpha"/>
<path layer="alpha" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path matrix="-1 0 0 1 256 0" stroke="red">
64 708 m
96 708
112 712
120 720
124 752
128 756
128 756 s
</path>
<path stroke="black" arrow="normal/normal">
128 700 m
128 768 l
</path>
<path stroke="black" arrow="normal/normal">
56 704 m
200 704 l
</path>
<path fill="yellow" tiling="rising">
192 708 m
176.003 708.077 l
176.111 704 l
192.168 704 l
192 708 l
192 708 l
</path>
<text transformations="translations" pos="176 696" stroke="yellow" type="label" width="4.311" height="4.289" depth="0" valign="baseline">$c$</text>
<text matrix="1 0 0 1 101.264 5.31508" transformations="translations" pos="64 712" stroke="yellow" type="label" width="35.5" height="6.227" depth="0" valign="baseline" size="small">Fl$\ddot a$che $\alpha$</text>
<text matrix="1 0 0 1 -8 -4" transformations="translations" pos="144 748" stroke="red" type="label" width="51.371" height="6.227" depth="0.83" valign="baseline" size="small">Fl$\ddot a$che $1-\alpha$</text>
<path stroke="orange" arrow="normal/normal">
176 692 m
212 692 l
</path>
<text matrix="1 0 0 1 -32 4" transformations="translations" pos="176 680" stroke="orange" type="label" width="55.875" height="3.468" depth="0.96" valign="baseline" size="tiny">Ablehnungsbereich</text>
<path stroke="turquoise" arrow="normal/normal">
176 692 m
64 692 l
</path>
<text transformations="translations" pos="76 684" stroke="turquoise" type="label" width="54.838" height="3.459" depth="0" valign="baseline" size="tiny">$Annahmebereich$</text>
<path fill="red" tiling="falling">
64 708 m
96 708
112 712
120 720
124 752
128 756
132 752
136 720
144 712
160 708
176.003 708.077
176.003 708.077
176.111 704
176.111 704
64 704
64 704
64 708 s
</path>
</page>
</ipe>
Write Preview
Loading…
Cancel
Save