Cours proba 2

Question 1

loi proba de X

pour discrete

Answer 1

p(X=xi) = pi

Question 2

loi proba de X

pour continue

Answer 2

P(X=x) = 0
P(X appartient [a;b]) = int de a->b f(x)dx
(f(x)>0)
pour loi unif = f(x) = k et k = 1 / b-a
pour loi exp f(x) = lambda exp (- lambdax)

Question 3

Fonction de repartion
F(X) = P(X≤x)
pour discrete

Answer 3

somme P(X=xi)

Question 4

Fonction de repartion
F(X) = P(X≤x)
pour continue

Answer 4

Loi uniforme 
F(x) = x-a/b-a
Loi exp 
F(X) = 1 - exp (- lambdax) 
P(X>x) =  exp (- lambdax)

Question 5

Esperance

discrete

Answer 5

somme x P(X=x)

Question 6

Esperance

continue

Answer 6

loi uniforme
E(X) = a+b /2
loi exp
1 / lambda

Question 7

calcule esperance
E(k)
E(kx)
E(K+X)

Answer 7

E(k) = k
E(kx) = k E(X)
E(K+X) = E(X)+k

Question 8

Variance

formule g

Answer 8

E(X^2) - (E(X))^2

Question 9

Variance

discrete

Answer 9

p(1-p)

Question 10

Variance

continue

Answer 10

loi unif
(b-a)^2 / 12
loi exp
1/ lambda^2

Question 11

calcul variance 
V(k) 
V(kx) 
V(K+X) 
V(ax +b)

Answer 11

V(k) = 0
V(kx) = k^2 V(X)
V(K+X) = Var(X)
V(ax +b) = a^2 Var(X)