\begin{exercice} On considère les courbes ci-dessous représentant les fonctions de densité de trois variables aléatoires $X$, $Y$ et $Z$ suivant les lois respectives $\mathscr{N}\left(6\ ;\ \nombre{2,5}^2\right)$, $\mathscr{N}\left(6\ ;\ \nombre{5}^2\right)$ et $\mathscr{N}\left(6\ ;\ \nombre{1}^2\right)$.

\begin{center}
\begin{tikzpicture}[general,xscale=0.5,yscale=11.3]
\draw[domain=0:12,epais,color=J1,samples=100] plot(\x,{(1/(2.5*2.5066))*exp((-1/(2*2.5*2.5))*(\x-6)*(\x-6))});
\draw[domain=0:12,epais,color=H1,samples=100] plot(\x,{(1/(5*2.5066))*exp((-1/(2*5*5))*(\x-6)*(\x-6))});
\draw[domain=0:12,epais,samples=100,color=A1] plot(\x,{(1/(1*2.5066))*exp((-1/(2*1*1))*(\x-6)*(\x-6))});
\axeX{0}{12}{};


\draw (0,0) node {{\small $+$}};
\draw (1,0) node {{\small $+$}};
\draw (2,0) node {{\small $+$}};
\draw (3,0) node {{\small $+$}};
\draw (4,0) node {{\small $+$}};
\draw (5,0) node {{\small $+$}};
\draw (6,0) node {{\small $+$}};
\draw (7,0) node {{\small $+$}};
\draw (8,0) node {{\small $+$}};
\draw (9,0) node {{\small $+$}};
\draw (10,0) node {{\small $+$}};
\draw (11,0) node {{\small $+$}};
\draw (12,0) node {{\small $+$}};

\draw (6,0) node [below] {$t$};

\draw (7.5,0.30) node [below] {$\mathscr{C}_1$};
\draw (9,0.15) node [below] {$\mathscr{C}_2$};
\draw (11.5,0.1) node [below] {$\mathscr{C}_3$};

%\axeY{0}{0.25}{};
\end{tikzpicture}
\end{center}
\vspace{-2\baselineskip}\begin{enumerate}
    \item Graphiquement, quelle est la valeur de $t$ ?
    \item Associer chacune des courbes à la variable aléatoire lui correspondant.
\end{enumerate}
\end{exercice}

