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En associant la valeur 1 à un succès et 0 à un échec. On peut modéliser cette expérience avec un variable aléatoire $X$ qui suit un \textbf{loi de Bernoulli} (notée $X \sim \mathcal{B}(p)$) résumée par le tableau suivant: @@ -40,7 +40,7 @@ Un passager qui a 9 chances sur 10 de se présenter à l'embarquement d'un avion Soit $X \sim \mathcal{B}$ alors \begin{itemize} \item L'espérance de $X$ est $E[X] = p$ - \item L'écart-type de $X$ est $\sigma = p(1-p)$ + \item L'écart-type de $X$ est $\sigma = \sqrt{p(1-p)}$ \end{itemize} \subsubsection*{Démonstration} @@ -48,11 +48,11 @@ Soit $X \sim \mathcal{B}$ alors \section{Loi binomiale} -On a vu que pour simuler tout un vol, c'est à dire 53 passagers, il fallait répéter 53 fois la loi de Bernoulli vue dans l'exemple précédent. Les répétitions de loi de Bernoulli s'appellent \textbf{schéma de Bernoulli} et sont modéliser avec une loi \textbf{binomiale}. +On a vu que pour simuler tout un vol, c'est à dire 53 passagers, il fallait répéter 53 fois l'épreuve de Bernoulli vue dans l'exemple précédent. Les répétitions d'épreuve de Bernoulli s'appellent \textbf{schéma de Bernoulli} et sont modéliser avec une loi \textbf{binomiale}. \subsection*{Définition} -La \textbf{loi Binomiale de paramètre $n$ et $p$} notée $\mathcal{B}(n;p)$ est la loi de probabilité qui modélise la répétition indépendantes et identiques de $n$ situations modélisées par une loi de Bernoulli de paramètre $p$. +La \textbf{loi Binomiale de paramètre $n$ et $p$} notée $\mathcal{B}(n;p)$ est la loi de probabilité qui modélise la somme de répétitions indépendantes et identiques de $n$ situations modélisées par une loi de Bernoulli de paramètre $p$. \bigskip