% proflycee-tools-probas.tex % Copyright 2023 Cédric Pierquet % Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt %%------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 } %%------Fonction de répartition \NewDocumentCommand\CrochetFctRepart{ m m }{ \draw[red,\FctRepartThickness] ({#1 + 0.1}, {#2 + 0.025}) -- (#1,#2 + 0.025) -- (#1,#2 - 0.025) -- ({#1 + 0.1}, {#2 - 0.025}); } \defKV[fctrepart]{% Couleur=\def\FctRepartColor{#1},% Epaisseur=\def\FctRepartThickness{#1},% Extremite=\def\FctRepartExtremite{#1} } \setKVdefault[fctrepart]{% Couleur=red,% Epaisseur=thick,% Pointilles=true,% Extremite=crochet } \NewDocumentCommand\FonctionRepartTikz{ O{} m }{% \restoreKV[fctrepart]% \setKV[fctrepart]{#1}% \setsepchar[.]{/.,}% \readlist*\ListeFonctRepart{#2}% \def\NbPortions{\ListeFonctRepartlen} \foreach \i in {1,2,...,\ListeFonctRepartlen} {% \IfStrEq{\ListeFonctRepart[\i,2]}{*}% {% \def\valxdeb{\xmin}% }% {% \itemtomacro\ListeFonctRepart[\i,2]\valxdeb% \IfStrEq{\FctRepartExtremite}{crochet}% { \CrochetFctRepart{\ListeFonctRepart[\i,2]}{\ListeFonctRepart[\i,1]}% }{}% \IfStrEq{\FctRepartExtremite}{point}% { \filldraw[\FctRepartColor] ({\valxdeb},{\ListeFonctRepart[\i,1]}) circle[radius=1.5pt] ;% }{}% }% \IfStrEq{\ListeFonctRepart[\i,3]}{*}% {% \def\valxfin{\xmax}% }% {% \itemtomacro\ListeFonctRepart[\i,3]\valxfin% \IfStrEq{\FctRepartExtremite}{crochet}% { \CrochetFctRepart{\ListeFonctRepart[\i,3]}{\ListeFonctRepart[\i,1]}% }{}% \IfStrEq{\FctRepartExtremite}{point}% { \draw[\FctRepartColor,fill=white] ({\valxfin},{\ListeFonctRepart[\i,1]}) circle[radius=1.5pt] ;% }{}% }% \ifboolKV[fctrepart]{Pointilles}% {% \xintifboolexpr{\valxdeb * \valxfin > 0 'and' \valxdeb > 0}% {% \draw[semithick,dashed] (0,{\ListeFonctRepart[\i,1]})--({\valxdeb},{\ListeFonctRepart[\i,1]}) ;% }{}% \xintifboolexpr{\valxdeb * \valxfin > 0 'and' \valxdeb < 0}% {% \draw[semithick,dashed] (0,{\ListeFonctRepart[\i,1]})--({\valxfin},{\ListeFonctRepart[\i,1]}) ;% }{}% }{}% \draw[\FctRepartThickness,\FctRepartColor] ({\valxdeb},{\ListeFonctRepart[\i,1]})--({\valxfin},{\ListeFonctRepart[\i,1]}) ;% }% } \endinput