Lois usuelles

Bernoulli

$X\hookrightarrow \mathcal{B}(p)$

Poisson

Uniforme

Géométrique

Binomiale

$X\hookrightarrow\mathcal{U}\lbrack1,n\rbrack$

$X\hookrightarrow\mathcal{G}(p)$

$X\hookrightarrow \mathcal{B}(n,p)$

$X(\Omega)= \lbrack 0,n\rbrack$

$E(X)=np$

$V(X)=npq$

$P(X=k) = \binom{n}{k}p^kq^{n-k},\space \forall k\in\lbrack0,n\rbrack$

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$X(\Omega)= \lbrace 0,1\rbrace$

$\forall t\in\mathbb{R},\space G_X(t)=(q+pt)^n$

$E(X)=p$

$V(X)=pq$

$P(X=1) = p$

$E(X)=\frac {n+1}{2}$

$V(X)=\frac {n²-1}{12}$

$P(X=k) = \frac{1}{n},\space \forall k\in\lbrack1,n\rbrack$

$E(X)=\frac{1}{p}$

$V(X)=\frac{q}{p^2}$

$\forall k\in\mathbb{N^*},\space P(X=k) = pq^{k-1}$

$X\hookrightarrow\mathcal{P}(\lambda)$

$E(X)=V(X)=\lambda$

$\forall k\in\mathbb{N},\space P(X=k) = e^{-\lambda}\cdot\frac{\lambda^k}{k!}$

$X(\Omega)=\mathbb{N}$

$X(\Omega)= \mathbb{N^*}$

$X(\Omega)= \lbrack 1,n\rbrack$

$\forall\vert t\vert<\frac{1}{q},\space G_X(t)=\frac{pt}{1-qt}$

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$Soient, p\in\lbrack 0,1\rbrack,\space q=1-p\space et\space n\in\mathbb{N^*}$

$\forall t\in\mathbb{R},\space G_X(t)=\frac{pt}{1-qt}$