2019-2020/TES/Probabilte_statistiques/Loi_densite/1P_tableur.tex

\documentclass[10pt,xcolor=table]{classPres}
%\usepackage{myXsim}


\usepackage{pgfplots}
\pgfplotsset{compat=1.7}
\pgfmathdeclarefunction{gauss}{2}{%
      \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
  }

\title{}
\author{}
\date{Févier 2020}

\begin{document}
\begin{frame}{Représentation de la loi binomiale} 
    \begin{enumerate}
        \item Rédiger une situation modélisable avec une loi binomiale.
        \item Construire avec le tableur le tableau des valeurs de cette loi.
            \begin{center}
                \texttt{LOI.BINOMIALE(k; n; p; 0)}
            \end{center}
        \item Représenter avec un diagramme barre ces probabilités
        \item Reporter dessus l'espérance et l'écart-type.
    \end{enumerate}
\end{frame}

\begin{frame}[fragile]{Loi binomiale vers la loi normale} 
    Dans ces 2 représentations $n = 40$.

    \begin{tikzpicture}[
        declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
        ]
        \begin{axis}[
            xscale=0.65,
            samples at={0,...,40},
            yticklabel style={
                /pgf/number format/fixed,
                /pgf/number format/fixed zerofill,
                /pgf/number format/precision=1
            },
            ybar=0pt, bar width=1
            ]
            %\addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)}; \addlegendentry{$p=0.2$}
            \node[draw=black,fill=white,anchor=north west] at (rel axis cs:0,1) {$p=0.5$};
            \addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)}; 
        \end{axis}
    \end{tikzpicture}
    \hfill
    \begin{tikzpicture}[
        declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
        ]
        \begin{axis}[
            xscale=0.65,
            samples at={0,...,40},
            yticklabel style={
                /pgf/number format/fixed,
                /pgf/number format/fixed zerofill,
                /pgf/number format/precision=1
            },
            ybar=0pt, bar width=1
            ]
            \node[draw=black,fill=white,anchor=north west] at (rel axis cs:0,1) {$p=0.2$};
            \addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)};
            %\addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)}; \addlegendentry{$p=0.5$}
        \end{axis}
    \end{tikzpicture}
\end{frame}

\begin{frame}[fragile]{Calculer probabilité} 
    Que représente  $P(X > 10)$?
    \hfill
    Comment interpréter $P(Y>10)$?


    \[
        X \sim \mathcal{B}(40;0.5) \qquad Y \sim \mathcal{N}(20; 10)
    \]

    \begin{tikzpicture}[
        declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
        ]
        \begin{axis}[
            xscale=0.6,
            yscale=0.9,
            samples at={0,...,40},
            yticklabel style={
                /pgf/number format/fixed,
                /pgf/number format/fixed zerofill,
                /pgf/number format/precision=2
            },
            enlargelimits=false, clip=false, axis on top,
            ybar=0pt, bar width=1
            ]
            %\addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)}; \addlegendentry{$p=0.2$}
            \addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)}; 
        \end{axis}
    \end{tikzpicture}
    \hfill
    \begin{tikzpicture}
        \begin{axis}[
            xscale=0.6,
            yscale=0.9,
            no markers, domain=0:40, samples=100,
            yticklabel style={
                /pgf/number format/fixed,
                /pgf/number format/fixed zerofill,
                /pgf/number format/precision=2
            },
            %axis lines*=left, xlabel=$x$, ylabel=$y$,
            %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=12cm,
            enlargelimits=false, 
            clip=false, axis on top,
            %grid = major
            ]
            \addplot [very thick,cyan!50!black] {gauss(20,3)};
        \end{axis}
    \end{tikzpicture}
\end{frame}
\end{document}

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