\begin{tikzpicture}
\begin{axis}[
xmin=-1, xmax=1,
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=0.6,
yticklabel style={yshift=0.5cm, xshift=0.8cm},
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={-1, 1},
ytick=0.5,
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]{
	-1.029 0.4681 \\
	-0.987 0.46555 \\
	-0.945 0.46698 \\
	-0.903 0.46238 \\
	-0.861 0.46662 \\
	-0.819 0.46579 \\
	-0.777 0.46467 \\
	-0.735 0.46533 \\
	-0.693 0.4645 \\
	-0.651 0.47183 \\
	-0.609 0.473 \\
	-0.567 0.47052 \\
	-0.525 0.47769 \\
	-0.483 0.47964 \\
	-0.441 0.4845 \\
	-0.399 0.47945 \\
	-0.357 0.4756 \\
	-0.315 0.48581 \\
	-0.273 0.48245 \\
	-0.231 0.48512 \\
	-0.189 0.48455 \\
	-0.147 0.48971 \\
	-0.105 0.49229 \\
	-0.062999 0.48376 \\
	-0.020999 0.48714 \\
	0.021001 0.48774 \\
	0.063 0.48517 \\
	0.105 0.48286 \\
	0.147 0.48495 \\
	0.189 0.49255 \\
	0.231 0.49062 \\
	0.273 0.48731 \\
	0.315 0.47883 \\
	0.357 0.48307 \\
	0.399 0.4764 \\
	0.441 0.47657 \\
	0.483 0.47974 \\
	0.525 0.47679 \\
	0.567 0.47707 \\
	0.609 0.47186 \\
	0.651 0.47183 \\
	0.693 0.46886 \\
	0.735 0.4711 \\
	0.777 0.46469 \\
	0.819 0.47233 \\
	0.861 0.47057 \\
	0.903 0.46924 \\
	0.945 0.46526 \\
	0.987 0.46519 \\
	1.029 0.46595 \\
};
\addplot[black, domain=-1:1, samples=2] {0.5};
\end{axis}
\end{tikzpicture}