129 lines
4.1 KiB
TeX
129 lines
4.1 KiB
TeX
\documentclass[10pt,xcolor=table]{classPres}
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%\usepackage{myXsim}
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\usepackage{pgfplots}
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\pgfplotsset{compat=1.7}
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\pgfmathdeclarefunction{gauss}{2}{%
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\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
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}
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\title{}
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\author{}
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\date{Févier 2020}
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\begin{document}
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\begin{frame}{Représentation de la loi binomiale}
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\begin{enumerate}
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\item Rédiger une situation modélisable avec une loi binomiale.
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\item Construire avec le tableur le tableau des valeurs de cette loi.
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\begin{center}
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\texttt{LOI.BINOMIALE(k; n; p; 0)}
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\end{center}
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\item Représenter avec un diagramme barre ces probabilités
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\item Reporter dessus l'espérance et l'écart-type.
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\end{enumerate}
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\end{frame}
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\begin{frame}[fragile]{Loi binomiale vers la loi normale}
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Dans ces 2 représentations $n = 40$.
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\begin{tikzpicture}[
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declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
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]
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\begin{axis}[
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xscale=0.65,
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samples at={0,...,40},
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yticklabel style={
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/pgf/number format/fixed,
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/pgf/number format/fixed zerofill,
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/pgf/number format/precision=1
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},
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ybar=0pt, bar width=1
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]
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%\addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)}; \addlegendentry{$p=0.2$}
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\node[draw=black,fill=white,anchor=north west] at (rel axis cs:0,1) {$p=0.5$};
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\addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)};
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\end{axis}
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\end{tikzpicture}
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\hfill
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\begin{tikzpicture}[
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declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
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]
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\begin{axis}[
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xscale=0.65,
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samples at={0,...,40},
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yticklabel style={
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/pgf/number format/fixed,
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/pgf/number format/fixed zerofill,
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/pgf/number format/precision=1
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},
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ybar=0pt, bar width=1
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]
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\node[draw=black,fill=white,anchor=north west] at (rel axis cs:0,1) {$p=0.2$};
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\addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)};
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%\addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)}; \addlegendentry{$p=0.5$}
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\end{axis}
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\end{tikzpicture}
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\end{frame}
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\begin{frame}[fragile]{Calculer probabilité}
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Que représente $P(X > 10)$?
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\hfill
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Comment interpréter $P(Y>10)$?
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\[
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X \sim \mathcal{B}(40;0.5) \qquad Y \sim \mathcal{N}(20; 10)
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\]
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\begin{tikzpicture}[
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declare function={binom(\k,\n,\p)=\n!/(\k!*(\n-\k)!)*\p^\k*(1-\p)^(\n-\k);},
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]
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\begin{axis}[
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xscale=0.6,
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yscale=0.9,
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samples at={0,...,40},
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yticklabel style={
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/pgf/number format/fixed,
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/pgf/number format/fixed zerofill,
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/pgf/number format/precision=2
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},
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enlargelimits=false, clip=false, axis on top,
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ybar=0pt, bar width=1
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]
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%\addplot [fill=cyan, fill opacity=0.5] {binom(x,40,0.2)}; \addlegendentry{$p=0.2$}
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\addplot [fill=orange, fill opacity=0.5] {binom(x,40,0.5)};
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\end{axis}
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\end{tikzpicture}
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\hfill
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\begin{tikzpicture}
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\begin{axis}[
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xscale=0.6,
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yscale=0.9,
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no markers, domain=0:40, samples=100,
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yticklabel style={
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/pgf/number format/fixed,
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/pgf/number format/fixed zerofill,
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/pgf/number format/precision=2
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},
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%axis lines*=left, xlabel=$x$, ylabel=$y$,
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%every axis y label/.style={at=(current axis.above origin),anchor=south},
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%every axis x label/.style={at=(current axis.right of origin),anchor=west},
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%height=5cm, width=12cm,
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enlargelimits=false,
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clip=false, axis on top,
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%grid = major
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]
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\addplot [very thick,cyan!50!black] {gauss(20,3)};
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\end{axis}
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\end{tikzpicture}
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\end{frame}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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