documentclass[]{article}

usepackage{pgfplotstable}
usepackage{pgfplots}

begin{document}
The C.D.F is as follows:

[F(x)=
begin{dcases}
0&text{$x<1$}\
frac{11}{36}&text{$1leq x<2$}\
frac{20}{36}&text{$2leq x<3$}\
frac{27}{36}&text{$3leq x<4$}\
frac{32}{36}&text{$4leq x<5$}\
frac{35}{36}&text{$5leq x<6$}\
1&text{$xgeq 6$}\
end{dcases}
]

The C.D.F can be graphed as follows:

{centering
begin{tikzpicture}
begin{axis}[
clip=false,
jump mark left,
ymin=0,ymax=1,
xmin=0, xmax=5,
every axis plot/.style={very thick},
discontinuous,
table/create on use/cumulative distribution/.style={
    create col/expr={pgfmathaccuma + thisrow{f(x)}}
}
]
addplot [red] table [y=cumulative distribution]{
x f(x)
0 0
1 11/36
2 20/36
3 27/36
4 32/36
5 35/36
6 1
};
end{axis}
end{tikzpicture}
par}
end{document}

documentclass[]{article}
usepackage{amsmath,mathtools}
usepackage{pgfplotstable}
usepackage{pgfplots}

begin{document}
The C.D.F is as follows:
[F(x)=
begin{dcases}
0&text{$x<1$}\
frac{11}{36}&text{$1leq x<2$}\
frac{20}{36}&text{$2leq x<3$}\
frac{27}{36}&text{$3leq x<4$}\
frac{32}{36}&text{$4leq x<5$}\
frac{35}{36}&text{$5leq x<6$}\
1&text{$xgeq 6$}\
end{dcases}
]

The C.D.F can be graphed as follows:
begin{center}
begin{tikzpicture}
begin{axis}[
clip=false,
jump mark left,
%ymin=0,ymax=1,
%xmin=0, xmax=5,
every axis plot/.style={very thick},
%discontinuous,
table/create on use/cumulative distribution/.style={
    create col/expr={pgfmathaccuma + thisrow{f(x)}}
}
]
addplot [red] table [y=cumulative distribution]{
x f(x)
0 0
1 11/36
2 20/36
3 27/36
4 32/36
5 35/36
6 1
};
end{axis}
end{tikzpicture}
end{center}
end{document}