Remove src/template
This commit is contained in:
parent
67a7f7acb9
commit
fe488b7d11
@ -1,308 +0,0 @@
|
||||
\ifdefined\ishandout
|
||||
\documentclass[de, handout]{CELbeamer}
|
||||
\else
|
||||
\documentclass[de]{CELbeamer}
|
||||
\fi
|
||||
|
||||
%
|
||||
%
|
||||
% CEL Template
|
||||
%
|
||||
%
|
||||
|
||||
\newcommand{\templates}{preambles}
|
||||
\input{\templates/packages.tex}
|
||||
\input{\templates/macros.tex}
|
||||
|
||||
\grouplogo{CEL_logo.pdf}
|
||||
|
||||
\groupname{Communication Engineering Lab (CEL)}
|
||||
\groupnamewidth{80mm}
|
||||
|
||||
\fundinglogos{}
|
||||
|
||||
%
|
||||
%
|
||||
% Custom commands
|
||||
%
|
||||
%
|
||||
|
||||
\input{lib/latex-common/common.tex}
|
||||
\pgfplotsset{colorscheme/rocket}
|
||||
|
||||
%TODO: Fix path
|
||||
\newcommand{\res}{src/template/res}
|
||||
|
||||
% \tikzstyle{every node}=[font=\small]
|
||||
% \captionsetup[sub]{font=small}
|
||||
|
||||
%
|
||||
%
|
||||
% Document setup
|
||||
%
|
||||
%
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{tikz-3dplot}
|
||||
\usetikzlibrary{spy, external, intersections}
|
||||
%\tikzexternalize[prefix=build/]
|
||||
|
||||
\usepackage{pgfplots}
|
||||
\pgfplotsset{compat=newest}
|
||||
\usepgfplotslibrary{fillbetween}
|
||||
|
||||
\usepackage{listings}
|
||||
\usepackage{subcaption}
|
||||
\usepackage{bbm}
|
||||
\usepackage{multirow}
|
||||
|
||||
\usepackage{xcolor}
|
||||
|
||||
\title{WT Tutorium 1}
|
||||
\author[Tsouchlos]{Andreas Tsouchlos}
|
||||
\date[]{\today}
|
||||
|
||||
%
|
||||
%
|
||||
% Document body
|
||||
%
|
||||
%
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{frame}[title white vertical, picture=images/IMG_7801-cut]
|
||||
\titlepage
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Aufgabe 1}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Theorie}
|
||||
|
||||
% TODO: Replace slide content with relevant stuff
|
||||
\begin{frame}
|
||||
\frametitle{Relevante Theorie I}
|
||||
|
||||
\begin{columns}
|
||||
\column{\kitthreecolumns}
|
||||
\begin{greenblock}{Zufallsvariablen (ZV)}%
|
||||
\vspace*{-6mm}
|
||||
\begin{gather*}
|
||||
f_X(x) := \frac{d}{dx} F_X(x) \\
|
||||
P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
|
||||
E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
|
||||
\end{gather*}
|
||||
\end{greenblock}
|
||||
|
||||
\column{\kitthreecolumns}
|
||||
\begin{greenblock}{Important Equations}%
|
||||
\vspace*{-6mm}
|
||||
\begin{gather*}
|
||||
f_X(x) := \frac{d}{dx} F_X(x) \\
|
||||
P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
|
||||
E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
|
||||
\end{gather*}
|
||||
\end{greenblock}
|
||||
\end{columns}
|
||||
|
||||
\begin{greenblock}{Normalverteilung}
|
||||
\begin{columns}
|
||||
\column{\kitthreecolumns}
|
||||
\begin{gather*}
|
||||
\text{Normalverteilung:} \hspace{8mm}
|
||||
f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
|
||||
e^{-\frac{(x - \mu)^2}{2\sigma^2}}
|
||||
\end{gather*}
|
||||
|
||||
\column{\kitthreecolumns}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
domain=-4:4,
|
||||
samples=100,
|
||||
width=11cm,
|
||||
height=6cm,
|
||||
ticks=none,
|
||||
xlabel={$x$},
|
||||
ylabel={$f_X(x)$}
|
||||
]
|
||||
\addplot+[mark=none, line width=1pt] {exp(-x^2)};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
\end{columns}
|
||||
\end{greenblock}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Aufgabe}
|
||||
|
||||
% TODO: Replace slide content with relevant stuff
|
||||
\begin{frame}
|
||||
\frametitle{2022H - Aufgabe 4}
|
||||
|
||||
Für die Planung und Konstruktion von Windkraftanlagen ist eine
|
||||
statistische Modellierung der
|
||||
Windgeschwindigkeit essentiell. Die absolute Windgeschwindigkeit
|
||||
kann als Weibull-verteilte
|
||||
Zufallsvariable V mit den Parametern $\beta > 0$ und $\theta > 0$
|
||||
modelliert werden. Die zugehörige
|
||||
Verteilungsfunktion ist%
|
||||
%
|
||||
\begin{gather*}
|
||||
F_V(v) = 1 - exp\left( -\left( \frac{v}{\theta} \right)^\beta
|
||||
\right), \hspace{3mm} v \ge 0
|
||||
\end{gather*}
|
||||
%
|
||||
|
||||
\begin{enumerate}
|
||||
\item Berechnen Sie die Wahrscheinlichkeitsdichte $f_V(v)$
|
||||
der Weibullverteilung.
|
||||
\item Eine Windkraftanlage speist Strom in das Stromnetz ein,
|
||||
wenn die absolute Windgeschwindigkeit größer als $4
|
||||
m/s$, jedoch kleiner als $25 m/s$ ist. Berechnen Sie die
|
||||
Wahrscheinlichkeit dafür, dass eine Windkraftanlage Strom
|
||||
einspeist, wenn die Windgeschwindigkeit Weibull-verteilt
|
||||
mit $\beta = 2,0$ und $\theta = 6,0$ ist.
|
||||
\item Eine Zufallsvariable W genüge einer Weibullverteilung
|
||||
mit $\beta = 1$ und $\theta = 3$. Ermitteln Sie den
|
||||
Erwartungsvert $E(W)$.
|
||||
\item Warum ist die Weibullverteilung für die Modellierung
|
||||
der absoluten Windgeschwindigkeit besser geeignet als
|
||||
eine Normalverteilung?
|
||||
\end{enumerate}
|
||||
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Aufgabe 2}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Theorie}
|
||||
|
||||
% TODO: Replace slide content with relevant stuff
|
||||
\begin{frame}
|
||||
\frametitle{Relevante Theorie II}
|
||||
|
||||
\begin{gather*}
|
||||
f_X(x) := \frac{d}{dx} F_X(x) \\
|
||||
P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
|
||||
E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
|
||||
\end{gather*}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[c]{0.5\textwidth}
|
||||
\centering
|
||||
\begin{gather*}
|
||||
\text{Normalverteilung:} \hspace{8mm}
|
||||
f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
|
||||
e^{-\frac{(x - \mu)^2}{2\sigma^2}}
|
||||
\end{gather*}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[c]{0.4\textwidth}
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
domain=-4:4,
|
||||
samples=100,
|
||||
width=\textwidth,
|
||||
height=0.5\textwidth,
|
||||
ticks=none,
|
||||
xlabel={$x$},
|
||||
ylabel={$f_X(x)$}
|
||||
]
|
||||
\addplot+[mark=none, line width=1pt] {exp(-x^2)};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{subfigure}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Aufgabe}
|
||||
|
||||
% TODO: Replace slide content with relevant stuff
|
||||
\begin{frame}
|
||||
\frametitle{2022H - Aufgabe 4}
|
||||
|
||||
Für die Planung und Konstruktion von Windkraftanlagen ist eine
|
||||
statistische Modellierung der
|
||||
Windgeschwindigkeit essentiell. Die absolute Windgeschwindigkeit
|
||||
kann als Weibull-verteilte
|
||||
Zufallsvariable V mit den Parametern $\beta > 0$ und $\theta > 0$
|
||||
modelliert werden. Die zugehörige
|
||||
Verteilungsfunktion ist%
|
||||
%
|
||||
\begin{gather*}
|
||||
F_V(v) = 1 - exp\left( -\left( \frac{v}{\theta} \right)^\beta
|
||||
\right), \hspace{3mm} v \ge 0
|
||||
\end{gather*}
|
||||
%
|
||||
|
||||
\begin{enumerate}
|
||||
\item Berechnen Sie die Wahrscheinlichkeitsdichte $f_V(v)$
|
||||
der Weibullverteilung.
|
||||
\item Eine Windkraftanlage speist Strom in das Stromnetz ein,
|
||||
wenn die absolute Windgeschwindigkeit größer als $4
|
||||
m/s$, jedoch kleiner als $25 m/s$ ist. Berechnen Sie die
|
||||
Wahrscheinlichkeit dafür, dass eine Windkraftanlage Strom
|
||||
einspeist, wenn die Windgeschwindigkeit Weibull-verteilt
|
||||
mit $\beta = 2,0$ und $\theta = 6,0$ ist.
|
||||
\item Eine Zufallsvariable W genüge einer Weibullverteilung
|
||||
mit $\beta = 1$ und $\theta = 3$. Ermitteln Sie den
|
||||
Erwartungsvert $E(W)$.
|
||||
\item Warum ist die Weibullverteilung für die Modellierung
|
||||
der absoluten Windgeschwindigkeit besser geeignet als
|
||||
eine Normalverteilung?
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Zusammenfassung}
|
||||
|
||||
% TODO: Replace slide content with relevant stuff
|
||||
\begin{frame}
|
||||
\frametitle{Zusammenfassung}
|
||||
|
||||
\begin{gather*}
|
||||
f_X(x) := \frac{d}{dx} F_X(x) \\
|
||||
P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
|
||||
E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
|
||||
\end{gather*}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[c]{0.5\textwidth}
|
||||
\centering
|
||||
\begin{gather*}
|
||||
\text{Normalverteilung:} \hspace{8mm}
|
||||
f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
|
||||
e^{-\frac{(x - \mu)^2}{2\sigma^2}}
|
||||
\end{gather*}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[c]{0.4\textwidth}
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
domain=-4:4,
|
||||
samples=100,
|
||||
width=\textwidth,
|
||||
height=0.5\textwidth,
|
||||
ticks=none,
|
||||
xlabel={$x$},
|
||||
ylabel={$f_X(x)$}
|
||||
]
|
||||
\addplot+[mark=none, line width=1pt] {exp(-x^2)};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{subfigure}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user