\section{Loi uniforme sur $\left[a\ ;\ b \right]$}

\begin{definition}
\begin{minipage}{0.6\linewidth}
Une variable aléatoire $X$ suit \MotDefinition[{La loi uniforme sur $\left[a\ ;\ b \right]$}]{la loi uniforme sur $\left[a\ ;\ b \right]$}[la loi uniforme sur]{} si elle admet pour densité la fonction  constante $f$ définie sur $\left[a\ ;\ b \right]$ par $f(x)=\dfrac{1}{b-a}$.

\end{minipage}
\hfill
\begin{minipage}{0.4\linewidth}

\begin{center}
  \begin{tikzpicture}[general,xscale=1,yscale=2]
\axeX{-0.5}{3}{};
\axeY{-0.3}{0.7}{};


\clip(-1.5,-0.3) rectangle (3,0.7);
\draw[smooth,samples=100,domain=0.5:2.5,color=B2] plot(\x,{0.5});
\draw (0.5,-0.1) node[below] {$a$};
\draw (2.5,-0.1) node[below] {$b$};
\draw (0,0.5) node[left] {$ \dfrac{1}{b-a} $};
\draw [dotted] (0.5,0.5)-- (0.5,0);
\draw [dotted] (2.5,0.5)-- (2.5,0);
\draw [dotted] (0.5,0.5)-- (0,0.5);

\begin{scriptsize}
\draw [color=black] (0.5,0)-- ++(-1.5pt,0 pt) -- ++(3.0pt,0 pt) ++(-1.5pt,-1.5pt) -- ++(0 pt,3.0pt);
\draw [color=black] (2.5,0)-- ++(-1.5pt,0 pt) -- ++(3.0pt,0 pt) ++(-1.5pt,-1.5pt) -- ++(0 pt,3.0pt);
\draw [color=black] (0,0.5)-- ++(-1.5pt,0 pt) -- ++(3.0pt,0 pt) ++(-1.5pt,-1.5pt) -- ++(0 pt,3.0pt);
\end{scriptsize}
\end{tikzpicture}
    \end{center}
\end{minipage}

\end{definition}

\vspace{-0.25\baselineskip}\begin{notation}
\og $X$ suit la loi uniforme sur $\left[a\ ;\ b \right]$ \fg{} s'écrit aussi \og $X$ suit la loi $\mathscr{U}\left(\left[a\ ;\ b \right]\right)$ \fg.
\end{notation}

