\begin{tikzpicture}
\begin{axis}[
name=plot1,
width=\textwidth,
height=0.5\textwidth,
axis lines*=middle,
enlargelimits = upper, clip=true,
scale only axis,
axis line style={->,>=stealth},
xlabel={\Large $x$},
ylabel={\Large $p_x(x)$},
every axis x label/.style={
	at={(ticklabel* cs:1)},
	xshift=-0.2cm,
	anchor=north,
},
every axis y label/.style={
	at={(ticklabel* cs:0.9)},
	xshift=0.7cm,
	anchor=south,
},
every outer x axis line/.append style={white!15!black},
every x tick label/.append style={font=\color{white!15!black}},
xmin=-3.00, xmax=3.4,
ymin=0, ymax=0.5,
ytick=\empty,
xtick={-2.5, -1.5, -0.5, 0.5, 1.5, 2.5},
xticklabels={\large $-\frac{5\Delta}{2}$, \large$-\frac{3\Delta}{2}$, \large$-\frac{\Delta}{2}$,\large $\frac{\Delta}{2}$, \large$\frac{3\Delta}{2}$, \large$\frac{5\Delta}{2}$},
xmajorgrids,
ymajorgrids,
every outer y axis line/.append style={white!15!black},
every y tick label/.append style={font=\color{white!15!black}},
legend style={draw=white!15!black,fill=white,legend cell align=left, at={(axis cs: 3, 0.25)}}]

\addplot [name path=g, smooth, black, line width=1.5pt, domain=-5:5, samples=51, forget plot] {gauss(x)};
\path[name path=axis1] (axis cs:-0.5,0) -- (axis cs:0.5,0);

\addplot [
thick,
color=black,
fill=black, 
fill opacity=0.10,
forget plot,
]
fill between[
of=g and axis1,
soft clip={domain=-0.5:0.5},
];

\node[black, fill=black!10, minimum size=1cm] at (axis cs: 1.75, 0.45) {\Large $\mathrm{Pr}(-\Delta/2 \leq x \leq \Delta/2)$};

\only<3-|handout:1>{
\addplot [dirac, line width=1.5pt] coordinates {(-2, 0.05) (-1, 0.15) (0, 0.3) (1, 0.15) (2, 0.05)}; \addlegendentry{\Large $p_{x_Q}(x)$};
}

\only<2-|handout:1>{
	\addplot [dirac, line width=1.5pt, forget plot] coordinates {(0, 0.3)};
}
\end{axis}
\end{tikzpicture}
