Distribución Exponencial

\documentclass{article}[14pt,a4paper]
% Comment the following line to NOT allow the usage of umlauts
\usepackage[utf8]{inputenc}
%\usepackage[english]{babel}
\usepackage[legalpaper, lmargin=1.8cm, rmargin=1.8cm, bottom=1.8cm]{geometry}
\usepackage{color}
% Uncomment the following line to allow the usage of graphics (.png, .jpg)
\usepackage{verbatim}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage[all]{xy}
\usepackage{pst-all}
\usepackage{tikz}
\usepackage{lscape}
\usepackage{tikzpeople}
\usepackage{fancybox}
\usepackage{cancel}
%\usepackage{gnuplottex}
%\usepackage{chronology}
\usepackage{pst-pdf}
%\usepackage{pstricks}

\usepackage{pst-solides3d}
\pagestyle{empty}
 \usetikzlibrary{datavisualization.formats.functions} \usetikzlibrary{matrix.skeleton} \usetikzlibrary[shapes,arrows,positioning,fit,backgrounds,intersections,shadows,calc] \usetikzlibrary{positioning} \usetikzlibrary{decorations.text} \usetikzlibrary{decorations.pathmorphing}
\usepackage{pgfplots} \pgfplotsset{width=10cm,compat=1.9}  \tikzset{flippedeventlabel/.append style={align=center}}
\usetikzlibrary{matrix.skeleton}
\usetikzlibrary[patterns,shapes,arrows,positioning,fit,backgrounds,intersections,shadows,calc]
\usetikzlibrary[datavisualization]
\usepackage{pgfplots}
\pgfplotsset{width=10cm,compat=1.9}
% Start the document

\begin{document}
%\pagecolor{black}

\tikz \datavisualization
[scientific axes=clean,
x axis={length=2.5cm, ticks={major at={
5,
6 as [style=red],
7 as [{style=blue, low=-1em}],
8 as [style=orange] $2^3$,
10 as [style=magenta]ten
}}},
visualize as line]
data [format=function] {
var x : interval [5:10];
func y = \value x * \value x;
};\\

\tikz \datavisualization
[scientific axes,
all axes={
length=3cm,
grid,
grid={minor steps between steps}
}, every major grid/.style = {style={blue, thin}},
visualize as line]
data [format=function] {
var x : interval [5:10];
func y = \value x * \value x;
};\\
%Definiendo Paquete de Funciones
\tikz \datavisualization data group {function classes} = {
data [set=log, format=function] {
var x : interval [0.2:2.5];
func y = ln(\value x);
}
data [set=lin, format=function] {
var x : interval [-2:2.5];
func y = \value x;
}
data [set=squared, format=function] {
var x : interval [-1.5:1.5];
func y = \value x*\value x;
}
data [set=exp, format=function] {
var x : interval [-2.5:1];
func y = exp(\value x);
}
data [set=cub, format=function] {
var x : interval [-1.5:1.5];
func y = \value x*\value x*\value x);
}
};
\tikz \datavisualization data group {Dist Exponencial} = {
data [set=Exp1, format=function] {
var x : interval [0:5];
func y = 0.5* exp(-0.5*\value x);
}
data [set=Exp2, format=function] {
var x : interval [0:5];
func y =exp(-\value x);
}
data [set=Exp3, format=function] {
var x : interval [0:5];
func y =1.5*exp(-1.5*\value x);
}
data [set=linev1, format=function] {
var y : interval [0:0.18394];
func x = 2;
}
data [set=linev2, format=function] {
var y : interval [0:0.36788];
func x = 1;
}
data [set=linev3, format=function] {
var y : interval [0:0.55182];
func x = 0.66666;
}
};
\tikz \datavisualization data group {Acum Exponencial} = {
data [set=AExp1, format=function] {
var x : interval [0:5];
func y = 1- exp(-0.5*\value x);
}
data [set=AExp2, format=function] {
var x : interval [0:5];
func y =1-exp(-\value x);
}
data [set=AExp3, format=function] {
var x : interval [0:5];
func y =1-exp(-1.5*\value x);
}
};
\begin{center}
\tikz \datavisualization [scientific axes,
visualize as smooth line/.list=
{log, lin, squared, exp,cub},
legend=south outside,
log= {label in legend={text=$\log x$}},
lin= {label in legend={text=$x/2$}},
squared={label in legend={text=$x^2$}},
exp= {label in legend={text=$e^x$}},
cub= {label in legend={text=$x^3$}},
style sheet=strong colors]
data group {function classes};\\
\vspace{0.5cm}
\begin{tikzpicture}
\draw node[blue]at (15,15) {Distribución Exponencial: $\mathsf{f(x) = \lambda e^{-\lambda x}}$,  \textcolor{red}{$\mathsf{x > 0}$}};

\end{tikzpicture}\\

\tikz \datavisualization
[scientific axes=clean,x axis={ticks={major at={
0 as [style=orange], 0.666 as [{style=blue, low=-1em}]$\frac{2}{3}$, 1 as [{style=red, low=-1em}], 2 as [{style=black, low=-1em}],
3 as [style=orange], 4 as [style=orange], 5 as [style=orange],}}},
visualize as smooth line/.list=
{Exp1, Exp2, Exp3, linev1, linev2, linev3},
legend = {south outside, label style = text colored,},
Exp1= {label in legend={text=$\lambda\to 0.5 $}},
Exp2= {label in legend={text=$\lambda \to 1$}},
Exp3={label in legend={text=$\lambda \to 1.5$}},
style sheet = strong colors]
data group {Dist Exponencial};\\

\begin{tikzpicture}

\draw node[blue]at (15,15) {Acumulada: $\mathsf{F(x) = 1\ -\  e^{-\lambda x}}$,  \textcolor{red}{$\mathsf{x > 0}$}};
\end{tikzpicture}\\

\tikz \datavisualization

[scientific axes,
visualize as smooth line/.list=
{AExp1, AExp2, AExp3},
legend = {south outside, label style = text colored,},
AExp1= {label in legend={text=$\lambda\to 0.5 $}},
AExp2= {label in legend={text=$\lambda \to 1$}},
AExp3={label in legend={text=$\lambda \to 1.5$}}, style sheet = strong colors]
data group {Acum Exponencial};
\end{center}
\end{document}