mathsprobasloisadensite.py

Created by condouarthur

Created on December 13, 2023

802 Bytes


Loi Uniforme continue sur [a;b]
Support : [a;b]
Densité 1/b-a
fonction de répartition 
F(x)= x-a/b-aII[a;b] + 1[b, +inf[
E(X)= a+b/2
V(X) = (b-a)2/12

Loi exponentielle
Utilisation : durée de survie d'un élément de survie d'un élément radioactif, d'une machine, sous hypothèse d'absence de vieillissement
Support R+
Densité Lambda exp(-lamdbax)
Fonction de répartition : F(x)=(1-exp(-Lambdax))
E(X)=Lambda
V(X)= Lambda2

Loi Gamma 
Utilisation Organisme vivant, contrat d'assurance, sévérité du risque. Cas de régression
Support R+
densité on rappelle Gamma (x) = int 0+inf exp(-t)t^x-1 dt
alors sa densité p^ax^a-1exp(-px)/Gamma(a)* IIR+
Fonction de répartition F(x)= p^a/Gamma(a) * int exp-pt t^x-1dt IIR+*
E(X) = a/p
V(x)= a/p2
Gamma(n+1)=n!=nGamma(n)

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