\begin{tikzpicture}
\begin{axis}[
xmin=-0.5,
xmax=0.5,
axis lines*=center,
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
%height=5cm, width=8cm,
xtick=\empty,
ytick=\empty,
xticklabel=\empty,
ymin=0,
ymax=1.2,
yticklabel style = {xshift=0.4cm, yshift=-0.2cm},
ylabel={\Large $p_{e}(e)$},
xlabel={\Large  $e$},
enlargelimits=false, clip=true, axis on top,
grid = major,
axis line style={->,>=stealth, shorten >= -10pt},
every axis x label/.style={
	at={(ticklabel* cs:1)},
	yshift=0.2cm,
	xshift=0.5cm,
	anchor=north,
},
every axis y label/.style={
	at={(ticklabel* cs:1)},
	anchor=south,
	xshift=0.3cm,
	yshift=0.3cm,
},
xtick={-0.5, 0.5},
ytick=1,
yticklabel style={yshift=0.6cm, xshift=0.3cm},
yticklabels={\Large $\frac{1}{\Delta}$},
xticklabels={\Large $-\frac{\Delta}{2}$, \Large $\frac{\Delta}{2}$},
]
\addplot[black, ybar interval, fill=black!20, mark=no] 
table[row sep=crcr]{
	-0.49 0.9955 \\
	-0.47 0.992 \\
	-0.45 0.9993 \\
	-0.43 0.99245 \\
	-0.41 1.0013 \\
	-0.39 1.0004 \\
	-0.37 1.0103 \\
	-0.35 0.99475 \\
	-0.33 0.99625 \\
	-0.31 0.99365 \\
	-0.29 1.0048 \\
	-0.27 0.98945 \\
	-0.25 0.9939 \\
	-0.23 1.0035 \\
	-0.21 1.0031 \\
	-0.19 1.0093 \\
	-0.17 0.9976 \\
	-0.15 0.9988 \\
	-0.13 0.99205 \\
	-0.11 1.0021 \\
	-0.09 1.0135 \\
	-0.07 1.0043 \\
	-0.05 0.9941 \\
	-0.03 0.9938 \\
	-0.0099997 1.0017 \\
	0.01 1.0011 \\
	0.03 1.0007 \\
	0.05 1.0078 \\
	0.07 1.0076 \\
	0.09 1.0083 \\
	0.11 1.003 \\
	0.13 1.002 \\
	0.15 1.0163 \\
	0.17 1.0009 \\
	0.19 0.9944 \\
	0.21 0.9965 \\
	0.23 1.0024 \\
	0.25 1.0056 \\
	0.27 0.98185 \\
	0.29 1.0019 \\
	0.31 0.99855 \\
	0.33 1.0045 \\
	0.35 1.0025 \\
	0.37 0.98935 \\
	0.39 0.9994 \\
	0.41 1.0028 \\
	0.43 0.98955 \\
	0.45 0.9975 \\
	0.47 1.0142 \\
	0.49 0.9937 \\
};

\addplot[black, domain=-1:1, samples=2] {1};
\end{axis}
\end{tikzpicture}