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Lois usuelles (Bernoulli (\(X\hookrightarrow \mathcal{B}(p)\) (\(E(X)=p\),…
Lois usuelles
Bernoulli
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\(X(\Omega)= \lbrace 0,1\rbrace\)
Poisson
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\(\forall t\in\mathbb{R},\space G_X(t)=\frac{pt}{1-qt}\)
Uniforme
\(X\hookrightarrow\mathcal{U}\lbrack1,n\rbrack\)
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\(P(X=k) = \frac{1}{n},\space \forall k\in\lbrack1,n\rbrack\)
\(X(\Omega)= \lbrack 1,n\rbrack\)
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Géométrique
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\(\forall\vert t\vert<\frac{1}{q},\space G_X(t)=\frac{pt}{1-qt}\)
Binomiale
\(X\hookrightarrow \mathcal{B}(n,p)\)
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\(P(X=k) = \binom{n}{k}p^kq^{n-k},\space \forall k\in\lbrack0,n\rbrack\)
\(X(\Omega)= \lbrack 0,n\rbrack\)
\(\forall t\in\mathbb{R},\space G_X(t)=(q+pt)^n\)
\(Soient, p\in\lbrack 0,1\rbrack,\space q=1-p\space et\space n\in\mathbb{N^*}\)