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|
% proflycee-tools-probas.tex
% Copyright 2023 Cédric Pierquet
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%%------LOISPROBAS
%calculs "simples"
\newcommand\CalcBinomP[3]{%npk
\xintFloatToDecimal{\xintfloateval{binomial(#1,#3)*#2^#3*(1-#2)^(#1-#3)}}
}
\newcommand\CalcBinomC[4]{%npab
\def\BorneInf{#3}\def\BorneSup{#4}
\ifthenelse{\equal{#3}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneSup{#1}}
{}
\xintFloatToDecimal{\xintfloateval{add(binomial(#1,i)*#2^i*(1-#2)^(#1-i), i=\BorneInf..\BorneSup)}}
}
\newcommand\CalcGeomP[2]{%pk
\xintFloatToDecimal{\xintfloateval{(1-#1)^(#2-1)*(#1)}}
}
\newcommand\CalcGeomC[3]{%pab
\def\BorneInf{#2}\def\BorneSup{#3}
\ifthenelse{\equal{#2}{*}}%
{\def\BorneInf{1}}
{}
\ifthenelse{\equal{#3}{*}}%
{\def\BorneSup{\fpeval{trunc(1/#1*10,0)}}}
{}
\xintFloatToDecimal{\xintfloateval{add((1-#1)^(i-1)*(#1), i=\BorneInf..\BorneSup)}}
}
\newcommand\CalcHypergeomP[4]{%Nnmk
\xintFloatToDecimal{\xintfloateval{binomial(#3,#4)*binomial(#1-#3,#2-#4)/binomial(#1,#2)}}
}
\newcommand\CalcHypergeomC[5]{%Nnmab
\def\BorneInf{#4}\def\BorneSup{#5}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneSup{#1}}
{}
\xintFloatToDecimal{\xintfloateval{add(binomial(#3,i)*binomial(#1-#3,#2-i)/binomial(#1,#2), i=\BorneInf..\BorneSup)}}
}
\newcommand\CalcPoissP[2]{%lk
\xintFloatToDecimal{\xintfloateval{exp(-#1)*#1^#2/factorial(#2)}}
}
\newcommand\CalcPoissC[3]{%lab
\def\BorneInf{#2}\def\BorneSup{#3}
\ifthenelse{\equal{#2}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#3}{*}}%
{\def\BorneSup{10*#1}}
{}
\xintFloatToDecimal{\xintfloateval{add(exp(-#1)*#1^i/factorial(i), i=\BorneInf..\BorneSup)}}
}
%utiles idée de https://tex.stackexchange.com/questions/355574/im-searching-for-a-table-with-cdf-of-standard-normal-distribution
\xintdeffloatvar a_1,a_2,a_3,a_4,a_5,a_6 :=
0.0705230784,0.0422820123,0.0092705272,0.0001520143,0.0002765672,0.0000430638;
\xintdeffloatvar rac2inv := sqrt(2)/2 ;
\xintdeffloatfunc erfc(x) := % uniquement pour x positif
((((((a_6*x+a_5)*x+a_4)*x+a_3)*x+a_2)*x+a_1)*x+1)**-16 ; % fin de définition de erfc(x)
\xintdeffloatfunc Phi(z) := (z>=0)?{1 - 0.5 * erfc(rac2inv * z)}{0.5 * erfc(-rac2inv * z)};
\newcommand\CalcNormC[4]{%msab
%def des bornes de l'intervalle suivant l'absence de a ou de b...
\def\BorneInf{#3}\def\BorneSup{#4}
\ifthenelse{\equal{#3}{*}}%
{\def\BorneInf{#4-10*#2}}
{}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneSup{#3+10*#2}}
{}
\xintFloatToDecimal{\xintfloateval{Phi((\BorneSup-#1)/#2)-Phi((\BorneInf-#1)/#2)}}
}
%calculs "simples" fiabilite
\newcommand\CalcExpoC[3]{%lab
\def\BorneInf{#2}\def\BorneSup{#3}
\ifthenelse{\equal{#2}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#3}{*}}%
{\def\BorneSup{100/#1}}
{}
\xintFloatToDecimal{\xintfloateval{exp(-#1*\BorneInf)-exp(-#1*\BorneSup)}}
}
%calculs formatés
\NewDocumentCommand{\BinomP}{ s O{3} m m m }{%*=sci,2=prec,3=n,4=p,5=k
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}}
}
}
\NewDocumentCommand{\BinomC}{ s O{3} m m m m }{%*=sci,2=prec,3=n,4=p,5=a,6=b
\def\BorneInf{#5}\def\BorneSup{#6}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#6}{*}}%
{\def\BorneSup{#3}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}}
}
}
\NewDocumentCommand{\GeomP}{ s O{3} m m }{%*=sci,2=prec,3=p,4=k
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}}
}
}
\NewDocumentCommand{\GeomC}{ s O{3} m m m }{%*=sci,2=prec,3=p,4=a,5=b
\def\BorneInf{#4}\def\BorneSup{#5}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneInf{1}}
{}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneSup{\fpeval{trunc(1/#3*10,0)}}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}}
}
}
\NewDocumentCommand{\HypergeomP}{ s O{3} m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=k
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}}
}
}
\NewDocumentCommand{\HypergeomC}{ s O{3} m m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=a,7=b
\def\BorneInf{#6}\def\BorneSup{#7}
\ifthenelse{\equal{#6}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#7}{*}}%
{\def\BorneSup{#3}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}}
}
}
\NewDocumentCommand{\PoissonP}{ s O{3} m m }{%*=sci,2=prec,3=lbda,4=k
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}}
}
}
\NewDocumentCommand{\PoissonC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b
\def\BorneInf{#4}\def\BorneSup{#5}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneSup{10*#3}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}}
}
}
\NewDocumentCommand{\NormaleC}{ s O{3} m m m m }{%
%*=ing,2=prec,3=mu,4=sigma,5=a,6=b
%def des bornes de l'intervalle suivant l'absence de a ou de b...
\def\BorneInf{#5}\def\BorneSup{#6}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneInf{#6-10*#4}}
{}
\ifthenelse{\equal{#6}{*}}%
{\def\BorneSup{#5+10*#4}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}}
}
}
\NewDocumentCommand{\ExpoC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b
\def\BorneInf{#4}\def\BorneSup{#5}
\ifthenelse{\equal{#4}{*}}%
{\def\BorneInf{0}}
{}
\ifthenelse{\equal{#5}{*}}%
{\def\BorneSup{100/#3}}
{}
\IfBooleanTF{#1}%
{%
\num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}}
}%
{%
\num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}}}
}
}
%%------ARBRESPROBAS
\defKV[PLTIKZARBRE]{%
Unite=\def\PLAPunite{#1},%
EspaceNiveau=\def\PLAPespniv{#1},%
EspaceFeuille=\def\PLAPespfeuille{#1},%
Type=\def\PLAPtype{#1},%
Police=\def\PLAPfont{#1},%
PoliceProbas=\def\PLAPfontproba{#1},%
StyleTrait=\def\PLAPtypetrait{#1},%
EpaisseurTrait=\def\PLAPeptrait{#1}
}
\setKVdefault[PLTIKZARBRE]{%
Unite=1cm,%
EspaceNiveau=3.25,%
EspaceFeuille=1,%
Type=2x2,%
Police=\normalfont\normalsize,%
PoliceProbas=\normalfont\small,%
InclineProbas=true,%
Fleche=false,%
StyleTrait={},%
EpaisseurTrait=semithick
}
\NewDocumentCommand\ArbreProbasTikz{ O{} m }{%1=options,2=libellés
\useKVdefault[PLTIKZARBRE]%
\setKV[PLTIKZARBRE]{#1}%
\setsepchar[.]{,./}%
\readlist*\PLARBREDONNES{#2}%
\begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite]
%styles
\tikzstyle{noeud} = [font=\PLAPfont]
\tikzstyle{probas}= [font=\PLAPfontproba]
\ifboolKV[PLTIKZARBRE]{InclineProbas}
{\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]}
{\tikzstyle{PLetiquette}=[pos=0.525,fill=white]}
\ifboolKV[PLTIKZARBRE]{Fleche}
{\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]}
{\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]}
%arbre2x2
\IfEq{\PLAPtype}{2x2}
{%
\coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (A12)--(A23) ;}
{\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
}{}
%arbre3x2
\IfEq{\PLAPtype}{3x2}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (A12)--(A23) ;}
{\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (R)--(A13) ;}
{\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A13)--(A25) ;}
{\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
\ifstrempty{\PLARBREDONNES[9,2]}
{\draw[PLfleche] (A13)--(A26) ;}
{\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
}{}
%arbre2x3
\IfEq{\PLAPtype}{2x3}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (A11)--(A23) ;}
{\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (A12)--(A25) ;}
{\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A12)--(A26) ;}
{\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
}{}
%arbre2x3
\IfEq{\PLAPtype}{3x3}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
\node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]};
\node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]};
\node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[9,2]}
{\draw[PLfleche] (R)--(A13) ;}
{\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
%N2
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (A11)--(A23) ;}
{\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (A12)--(A25) ;}
{\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A12)--(A26) ;}
{\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
\ifstrempty{\PLARBREDONNES[10,2]}
{\draw[PLfleche] (A13)--(A27) ;}
{\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;}
\ifstrempty{\PLARBREDONNES[11,2]}
{\draw[PLfleche] (A13)--(A28) ;}
{\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;}
\ifstrempty{\PLARBREDONNES[12,2]}
{\draw[PLfleche] (A13)--(A29) ;}
{\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;}
}{}
\end{tikzpicture}
}
\NewDocumentEnvironment{EnvArbreProbasTikz}{ O{} m }%1=options,2=libellés
{
\useKVdefault[PLTIKZARBRE]
\setKV[PLTIKZARBRE]{#1}
\setsepchar[.]{,./}%
\readlist*\PLARBREDONNES{#2}
\begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite]
%styles
\tikzstyle{noeud} = [font=\PLAPfont]
\tikzstyle{probas}= [font=\PLAPfontproba]
\ifboolKV[PLTIKZARBRE]{InclineProbas}
{\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]}
{\tikzstyle{PLetiquette}=[pos=0.525,fill=white]}
\ifboolKV[PLTIKZARBRE]{Fleche}
{\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]}
{\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]}
%arbre2x2
\IfEq{\PLAPtype}{2x2}
{%
\coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (A12)--(A23) ;}
{\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
}{}
%arbre3x2
\IfEq{\PLAPtype}{3x2}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (A12)--(A23) ;}
{\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (R)--(A13) ;}
{\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A13)--(A25) ;}
{\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
\ifstrempty{\PLARBREDONNES[9,2]}
{\draw[PLfleche] (A13)--(A26) ;}
{\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
}{}
%arbre2x3
\IfEq{\PLAPtype}{2x3}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (A11)--(A23) ;}
{\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (A12)--(A25) ;}
{\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A12)--(A26) ;}
{\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
}{}
%arbre2x3
\IfEq{\PLAPtype}{3x3}
{%
%sommets
\coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ;
\node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
\node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
\node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
\node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
\node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
\node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
\node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
\node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
\node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
\node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]};
\node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]};
\node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]};
%branches
\ifstrempty{\PLARBREDONNES[1,2]}{}
{\draw[PLfleche] (R)--(A11) ;}
{\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
\ifstrempty{\PLARBREDONNES[5,2]}{}
{\draw[PLfleche] (R)--(A12) ;}
{\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
\ifstrempty{\PLARBREDONNES[9,2]}{}
{\draw[PLfleche] (R)--(A13) ;}
{\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
%N2
\ifstrempty{\PLARBREDONNES[2,2]}
{\draw[PLfleche] (A11)--(A21) ;}
{\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
\ifstrempty{\PLARBREDONNES[3,2]}
{\draw[PLfleche] (A11)--(A22) ;}
{\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
\ifstrempty{\PLARBREDONNES[4,2]}
{\draw[PLfleche] (A11)--(A23) ;}
{\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
\ifstrempty{\PLARBREDONNES[6,2]}
{\draw[PLfleche] (A12)--(A24) ;}
{\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
\ifstrempty{\PLARBREDONNES[7,2]}
{\draw[PLfleche] (A12)--(A25) ;}
{\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
\ifstrempty{\PLARBREDONNES[8,2]}
{\draw[PLfleche] (A12)--(A26) ;}
{\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
\ifstrempty{\PLARBREDONNES[10,2]}
{\draw[PLfleche] (A13)--(A27) ;}
{\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;}
\ifstrempty{\PLARBREDONNES[11,2]}
{\draw[PLfleche] (A13)--(A28) ;}
{\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;}
\ifstrempty{\PLARBREDONNES[12,2]}
{\draw[PLfleche] (A13)--(A29) ;}
{\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;}
}{}
}
{
\end{tikzpicture}
}
%%------SCHEMASPROBAS
%densites utiles
\def\densnorm#1{1/(sqrt(2*pi))*exp(-0.5*(#1*#1))}
\def\densexpo#1{exp(-#1)}
\defKV[GRPHPROBCONTINUES]{%
CouleurAire=\def\GRPHPROBcoulsurf{#1},%
CouleurCourbe=\def\GRPHPROBcoulcbe{#1},%
Largeur=\def\GRPHPROBlarg{#1},%
Hauteur=\def\GRPHPROBhauteur{#1}
}
\setKVdefault[GRPHPROBCONTINUES]{%
CouleurAire=LightGray,%
CouleurCourbe=red,%
Largeur=2,%
Hauteur=1,%
AfficheM=true,%
AfficheCadre=true
}
\NewDocumentCommand\LoiNormaleGraphe{ O{} D<>{} m m m m }{%1=options,2=optionstikz,3=m,4=s,5=a,6=b
%simplekv
\useKVdefault[GRPHPROBCONTINUES]%
\setKV[GRPHPROBCONTINUES]{#1}%
%unites
\def\UNITEX{\fpeval{\GRPHPROBlarg/8}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/0.5}}%
%bornes
\def\BorneInf{\fpeval{(#5-#3)/#4}}\def\BorneSup{\fpeval{(#6-#3)/#4}}%
\ifthenelse{\equal{#5}{*}}{\def\BorneInf{-4}}{}%
\ifthenelse{\equal{#6}{*}}{\def\BorneSup{4}}{}%
%tikzpicture
\begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2]
\ifboolKV[GRPHPROBCONTINUES]{AfficheM}%
{\draw (0,-0.0375) node[font=\tiny,scale={2*\UNITEX}] {#3} ;}
{}
\ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}%
{\draw[Gray] (-4,-0.075) rectangle (4,0.425) ;}
{}
\clip (-4,-0.075) rectangle (4,0.425) ;
\draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{\densnorm{\x}}) -- ({\BorneSup},0) -- cycle;
\draw[thick,->,>=latex] (-4,0)--(4,0) ;
\draw[thick,densely dotted] (0,0)--(0,0.39894) ;
\draw[thick,domain=-4:4,samples=100,\GRPHPROBcoulcbe] plot (\x,{\densnorm{\x}}) ;
\end{tikzpicture}
}
\NewDocumentCommand\LoiExpoGraphe{ O{} D<>{} m m m }{%1=options,2=optionstikz,3=l,4=a,5=b
%simplekv
\useKVdefault[GRPHPROBCONTINUES]%
\setKV[GRPHPROBCONTINUES]{#1}%
%unites
\def\UNITEX{\fpeval{\GRPHPROBlarg/4}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/1}}%
\def\MOYENNE{\fpeval{trunc(1/#3,0)}}%
%bornes
\def\BorneInf{\fpeval{#3*#4}}\def\BorneSup{\fpeval{#3*#5}}%
\ifthenelse{\equal{#4}{*}}{\def\BorneInf{0}}{}%
\ifthenelse{\equal{#5}{*}}{\def\BorneSup{4}}{}%
%tikzpicture
\begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2]
\ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}%
{\draw[Gray] (-0.2,-0.15) rectangle (3.8,0.85) ;}
{}
\clip (-0.2,-0.15) rectangle (3.8,0.85) ;
\draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{0.7*\densexpo{\x}}) -- ({\BorneSup},0) -- cycle;
\ifboolKV[GRPHPROBCONTINUES]{AfficheM}%
{\draw (1,-0.075) node[font=\tiny,scale={\UNITEX}] {\MOYENNE} ;
\draw[thick,densely dotted] (1,0)--(1,{0.7*\densexpo{1}}) ;}
{}
\draw[thick,->,>=latex] (-0.2,0)--(3.8,0) ;
\draw[thick,->,>=latex] (0,-0.15)--(0,0.85) ;
\draw[thick,domain=0:3.8,samples=100,\GRPHPROBcoulcbe] plot (\x,{0.7*\densexpo{\x}}) ;
\end{tikzpicture}
}
%%------aNp/Cnp
\NewDocumentCommand\CalculAnp{ m m }{%avec et pour xint, p/n
pfactorial(#2-#1,#2)
}
\NewDocumentCommand\CalculCnp{ m m }{%avec et pour xint, p/n
binomial(#2,#1)
}
\setKVdefault[anpCnp]{%
Formule=false,%
Notation=false,%
NotationAncien=false
}
\NewDocumentCommand\Arrangement{ s O{} m m }{%p/n
\useKVdefault[anpCnp]%
\setKV[anpCnp]{#2}%
\ifboolKV[anpCnp]{Notation}{A_{#4}^{#3}=}{}%
\ifboolKV[anpCnp]{Formule}{\frac{#4!}{\inteval{#4-#3}!}=}{}%
\IfBooleanTF{#1}%
{\xinteval{\CalculAnp{#3}{#4}}}%non formaté
{\num{\xinteval{\CalculAnp{#3}{#4}}}}%formaté
}
\NewDocumentCommand\Combinaison{ s O{} m m }{%p/n
\useKVdefault[anpCnp]%
\setKV[anpCnp]{#2}%
\ifboolKV[anpCnp]{Notation}{\binom{#4}{#3} =}{}%
\ifboolKV[anpCnp]{NotationAncien}{C_{#4}^{#3}=}{}%
\ifboolKV[anpCnp]{Formule}{\frac{#4!}{#3! \times \inteval{#4-#3}!}=}{}%
\IfBooleanTF{#1}%
{\xinteval{\CalculCnp{#3}{#4}}}%non formaté
{\num{\xinteval{\CalculCnp{#3}{#4}}}}%formaté
}
\endinput
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