03b_formulaire_proba_psy
!
Formulaire*de*probabilités*
!
!
1.!Formules*de*calcul*des*probabilités*
*
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)(1)(
)()()()(
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CC
C
BAPBAP
BAPBPAPBAP
APAP
∩−=∪
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−=
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A et B sont indépendants ssi P(A∩B)=P(A).P(B)
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2.!Variables*aléatoires*:*généralités*
*
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ρ
σσσσ
µµ
ρ
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+ = +
et 2
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2 2
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!
3.!Variables*aléatoires*:*lois*classiques*
*
*
Nom*
Valeurs*possibles*
ou*Domaine*
P(X=x)*
ou*densité*
Moyenne*
E(X)*
Variance*
V(X)*
J/.>#$%(!*.)-$?0(!
G!~*JKL,:=M!
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9Q=!
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L=;P9MQ9;!
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J/.>#$%(!F#/0./&(!
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σ
µ
σπ
−
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=
x
exf
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µ!
!!
σS!
*
4.!Calcul*de*probabilité*sur*une*variable*aléatoire*Normale*
*
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σ
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σµ
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x
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σµ
pp zx +=
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5.!Combinaison*linéaire*de*variables*aléatoires*Normales*
*
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_<!Somme*et*moyenne*de*variables*aléatoires*iid*L*Théorème*central*limite!
*
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* *
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a<!Théorème*central*limite*appliqué*à*la*variable*aléatoire*Binomiale!
*
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