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+\documentclass[varwidth=true, border=4pt]{article}
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+\usepackage[active,tightpage]{preview}
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+\usepackage[latin1]{inputenc}
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+\usepackage{amsmath}
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+\usepackage{pgfplots}
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+\usepackage{helvet}
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+\usepackage[eulergreek]{sansmath}
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+
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+\def\cdf(#1)(#2)(#3){0.5*(1+(erf((#1-#2)/(sqrt(#3*2)))))}%
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+% to be used: \cdf(x)(mean)(variance)
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+
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+\DeclareMathOperator{\CDF}{cdf}
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+
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+\pgfplotsset{
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+tick label style = {font=\sansmath\sffamily},
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+every axis label/.append style={font=\sffamily\footnotesize},
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+}
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+
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+\begin{document}
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+\begin{preview}
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+\begin{tikzpicture}
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+ \begin{axis}[
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+ width=13.5cm,
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+ height=8.625cm,
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+ % Grid
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+ grid = major,
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+ grid style={black, thin},
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+ % size
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+ xmin=-5.25, % start the diagram at this x-coordinate
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+ xmax= 5.25, % end the diagram at this x-coordinate
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+ ymin=-0.05, % start the diagram at this y-coordinate
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+ ymax= 1.05, % end the diagram at this y-coordinate
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+ % Legende
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+ legend pos=north west,
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+ legend style={font=\footnotesize},
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+ % Ticks
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+ tick align=inside,
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+ minor tick num=3,
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+ minor tick style={thick},
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+ yticklabel style={
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+ /pgf/number format/precision=1,
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+ /pgf/number format/fixed,
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+ /pgf/number format/fixed zerofill},
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+ % Axis
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+ axis line style = very thick,
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+ xlabel=$x$,
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+ x label style={at={(axis description cs:0.5,0)},
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+ anchor=north,
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+ font=\boldmath\Large},
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+ ylabel=$\Phi_{\mu, \sigma^2}(x)$,
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+ y label style={at={(axis description cs:0.05,0.5)},
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+ anchor=south,
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+ font=\boldmath\Large},
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+ ]
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+ \addplot[domain=-5.25:5.25,smooth,blue!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(0.2)};
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+ \addplot[domain=-5.25:5.25,smooth,red!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(1.0)};
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+ \addplot[domain=-5.25:5.25,smooth,yellow!80!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(5)};
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+ \addplot[domain=-5.25:5.25,smooth,green!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(-2)(0.5)};
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+ \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 0.2$}
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+ \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 1.0$}
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+ \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 5.0$}
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+ \addlegendentry{$\mu=-2,\quad \sigma^2 = 0.5$}
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+ \end{axis}
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+\end{tikzpicture}
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+\end{preview}
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+\end{document}
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