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z*Z=P=qQ`B(B0H6#$49UE9?94L{<`}vbM@AD$7+@x6sLC3&erHt$12e)$|<)}9sZhd ze5ig27hdSV$EmIPB~{RW4If5(E~z8BvKLqP|0G)K^s@M=_4ELyBANWnU*5`armh#Z f<2A(-^mIapODamE6bDy`A5BA5N9E-y^ML;k2#y!= literal 0 HcmV?d00001 diff --git a/sections/simulation.tex b/sections/simulation.tex index 3796735..4bf0eb6 100644 --- a/sections/simulation.tex +++ b/sections/simulation.tex @@ -1 +1,39 @@ -\section{Simulation} \ No newline at end of file +\section{Simulation} +\subsection{Monte Carlo Simulation} +Monte Carlo Simulation ist eine numerische Methode für statistische Simulation, die Sequenzen von Zufallszahlen benutzt, um die Simulation durchzuführen. + +\textbf{Eigenschaften:} +\begin{compactitem} + \item Monte Carlo Simulation ist ein kräftiges Instrument, um komplexe statistische Analysen durchzuführen und Wahrscheinlichkeiten und Verteilungen zu schätzen. + \item Es verlangt ein Systemmodell (quantitative Systembeschreibung). + \item Es werden (virtuelle) Experimente mit dem System ausgeführt, um Schlussfolgerungen bzgl. deren Verhalten zu ziehen. +\end{compactitem} + +\begin{example} + Berechne den Wert von $\pi$ + \begin{multicols}{5} + Fläche Rechteck: $(2r)^2$ \\ + Fläche Kreis: $\pi r^2$ \\ + $\frac{\text{Fläche Rechteck}}{\text{Fläche Kreis}}$: $\frac{4}{\pi}$ \\ + $\pi$: $4 * \frac{\text{Fläche Kreis}}{\text{Fläche Rechteck}}$ \\ + $\pi$: $4 * \frac{\text{Punkte im Kreis}}{\text{Punkte im Rechteck}}$ + \end{multicols} + \begin{minipage}[h]{0.825\textwidth} + \begin{lstlisting}[mathescape=true, tabsize=2] +N Punkte $X_i$ = -1 + 2$A_i$ und +N Punkte $Y_i$ = -1 + 2$B_i$ mit A, B Sequenzen von unabhaengigen Zufallszahlen +K = 0 + for i = 1 : N + if ($X_i^2$ + $Y_i^2$ < 1) + K = K + 1 + end +end + \end{lstlisting} + \end{minipage} + \begin{minipage}[h]{0.175\textwidth} + \includegraphics[width=1\textwidth]{pictures/montecarlopi} + \end{minipage} + $\pi = \frac{4*K}{N}$ +\end{example} + +\subsection{Diskrete Ereignissimulation}