CCCPaste

Abstract about Binomial

\documentclass{article}[14pt,a4paper]
% Comment the following line to NOT allow the usage of umlauts
%\usepackage[utf8]{inputenc}
%\useusepackage[utf8]{imputenc} %\usepackage[a4paper, lmargin=2cm, rmargin=2cm, bottom=2cm]{geometry}
\usepackage{color}
% Uncomment the following line to allow the usage of graphics (.png, .jpg)
\usepackage{multicol} \usepackage{verbatim} \usepackage{graphicx} \usepackage{amsmath} \usepackage[all]{xy} \usepackage{pst-all} \usepackage{tikz} \usepackage{gnuplottex} \usepackage{pst-pdf}
\usepackage{mathtools,amssymb}
\usepackage{xcolor}
\usepackage{tikz-3dplot}
%\usepackage[colorlinks=true,linkcolor=magenta,citecolor=blue,filecolor=magenta,url(color=blue]{hyperref} \urlstyle{same}
%\usepackage{chronology}
%\usepackage{pst-solides3d}
\tikzset{flippedeventlabel/.append style={align=center}} \usetikzlibrary{datavisualization} \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}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
%\psset{viewpoint=10 18 60 rtp2xyz,Decran=10,fontsize=10,unit=0.65cm}
\usetikzlibrary{patterns}
\pgfmathdeclarefunction{gauss}{2}{\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(#2^2))} }
\pgfmathdeclarefunction{gauss1}{2}{\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-(((1.2*x-#1)+1)^2)/(#2^2))} }
\pgfmathdeclarefunction{gauss2}{2}{\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-(((1.2*x-#1)-1)^2)/(#2^2))} }
% Start the document
\begin{document}
\pagecolor{red!20}
\begin{center}
\tdplotsetmaincoords{10}{110}
\begin{tikzpicture}[scale=1.5]

\draw [white] node at (3,1){\textbf{\textcolor{green}{\Huge{Función de Densidad Binomial}}}};
\draw [white] node at (3,-0.5)
{
\begin{minipage}{13cm}\textcolor{white}{\huge{Sea $\mathsf{X}$ la variable aleatoria que mide la cantidad de éxitos $\mathsf{x}$, con probabilidad $\mathsf{p}$, que se obtienen en $\mathsf{n}$ ensayos de Bernoulli, y recordando que $\mathsf{\binom{n}{x}=\frac{n!}{x!(n-x)!}}$, entonces:}}\\
\end{minipage};
};

\draw [white] node at (3,-2){\textbf{\huge{$\mathsf{P(X = x) = f(x)\ = \binom{n}{x}\ p^x\ (1-p)^{n-x}}$ }}};

\draw [white] node at (3,-3){\textbf{\textcolor{green}{\Huge{Función Acumulada Binomial}}}};

\draw [white] node at (3,-4){\textbf{\huge{$\mathsf{\displaystyle{P(X \leq x) = F(x)\ = \Sigma_{k=0}^{x}\ \binom{n}{k}\ p^k\ (1-p)^{n-k}}}$ }}};
\draw [white] node at (3,-6)
{
\begin{minipage}{13cm}\textcolor{white}{\huge{De acuerdo al cálculo del primer y segundo momento se obtiene que:
\begin{itemize}
\item Media: $\mathsf{\mu\ =\ np}$
\item Varianza: $\mathsf{\sigma^2\ =\ np(1-p)}$
\end{itemize}
}}
\end{minipage};
};

\end{tikzpicture}

\end{center}

\begin{tikzpicture}[scale =1,information text/.style={rounded corners=7pt,inner sep=2ex}]
\shadedraw (0,5)[xshift=1.85cm] node[left,text width=10cm, information text,scale=1,left color=red,right color=magenta] {\begin{minipage}{10cm}\bf\color{white} \tikz \draw (0,0) node[fill=black,text width=9.5cm] {\textcolor{white}{La aproximación parte de la relación binomial $\mathsf{\mu\ =\ np}$
y toma como objetivo la forma $\mathsf{p\ =\ \frac{\mu}{n}}$.}\\
\vspace{0.3cm}
\Large{Si $x_1, x_2, \cdots, x_n$ es una muestra aleatoria, en donde $x_i \sim \textit{N}(\mu, \sigma)$ para todo $i$. Entonces Y, definida mediante: $$ \displaystyle{y = \Sigma_{i=1}^n \left(\frac{x_i - \mu}{\sigma}\right)^2}$$}
posee una distribución Chi-Cuadrado con $n$ grados de libertad, en símbolos: $$Y\ \sim \ \chi^2(n)$$


\vspace{0.3cm}

};
\end{minipage}};
\end{tikzpicture}\\

\begin{tikzpicture}[scale=1.2]
\begin{axis}[legend style={rounded corners,fill=brown!40, visualize as smooth line},legend pos=outer north east, view={45}{35}]
\foreach \t in {0.6,0.65,0.7,0.75}
{
\pgfmathsetmacro{\s}{\t}
\addplot3[color=red, domain=0:15,samples=45,mesh,very thick] ({\s*cos(deg(x))},{\s*sin(deg(x))},{0.4*x });}

\draw [green,fill](6,6,21)circle(1.5pt);
\draw (6,6,21) node[green,left]{\tiny{21}};

\end{axis}
\end{tikzpicture}

%\draw [white] node at (4.3,0.3){\bf{\Large{$\mathbf{\Sigma}(\mathbf{x_k} - \overline{\mathbf{x}})^3 = 0$}}};

%\begin{axis}[blue, domain=0:30, samples=100, height=5cm, width=10cm, ytick=\empty, xtick=\empty, enlargelimits=false, clip=false]

%\addplot [very thick, white, domain=-3:3] {gauss1(0,1.2)} ;
%\addplot [very thick, white, domain=-3:3] {gauss2(0,1.2)} ;
%\addplot [very thick, white, domain=-3:3] {gauss(0,1)} ;
%\end{axis}

%Uncomment the following two lines if you want to have a bibliography1 %\bibliographystyle{alpha} %\bibliography{document} %\begin{thebibliography}{document} %\renewcommand %\refname{BIBLIOGRAFIA} %\bibitem{Baz} \textit{Bazaraa, M.S., J.J. %Jarvis} y \textit{H.D. Sheraly}, %\textit{Programación lineal y flujo de redes}, %Segunda Edición. Limusá, México, DF. 2004. %\end{thebibliography}
\end{document}