\documentclass{standalone}
 
\usepackage{pgfplots}
 
\pgfplotsset{compat = newest}
 
\begin{document}


\begin{tikzpicture}


\begin{axis}[
    xmin = -1, xmax = 4,
    ymin = -0.5, ymax = 2.50,
    axis lines = center,
    xlabel = $\sigma$,
    ylabel = {$\mu$},
]

\addplot [
    domain=-2:5, 
    samples=200, 
    color=orange,
]
{(1/(2*pi*0.2^2)^0.2)*exp(-(x-2)^2/(2*0.2^2))};

\addplot [
    domain=-2:5, 
    samples=200, 
    color=blue,
    ]
    {1/(2*pi*0.5^2)^0.5)*exp(-(x-0.9)^2/(2*0.5^2))};

\end{axis}
\end{tikzpicture}


\end{document}