\documentclass{standalone}
\standaloneconfig{border=2mm 2mm 2mm 2mm}
\usepackage{pgfplots}
\begin{document}

\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}

\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
  mark=none,domain=-2:3,samples=50,smooth}, % All plots: from -2:2, 50 samples, smooth, no marks
  axis x line*=bottom, % no box around the plot, only x and y axis
  axis y line*=left, % the * suppresses the arrow tips
  enlargelimits=upper] % extend the axes a bit to the right and top
  \addplot {gauss(0,0.5)};
  \addplot {gauss(1,0.75)};
\end{axis}
\node[above right] at (3,5) {$\mu$: la moyenne de la distribution};
\node[above right] at (3,4.5) {$\sigma$: l'ecart-type};
\node[above right] at (3,3.7) {$f_{(\sigma,\mu)}(x)=\frac{1}{\sigma\sqrt{2\pi}} \cdot e^{-\frac{(x-\mu)^2}{2\sigma^2}}$};

\end{tikzpicture}
\end{document}