Feuille d`exercices : Probabilités et Variables aléatoires finies.

r n
r+n−1
r n
d
3A, B, C
3
0,35 A
0,40 B
0,25 C
R
10%
R A 40%
B80% C J
A
B
C
n Fn
Fn=Xn
nXn
n p|Fn−1
6|<0,99≥0,99.
n2
1n
X
X(Ω) p(X > k)X
N1N n
1N n
Y
n
Y
[Y≥k]p0[Y≥k])
Y
n−2
X
Y X
Y
a)r
n+r×r−1 n+r−1b)r n+r×n n+r−1.
a)n
n+rb)d+n d+n+r.
a)8,8608 ×10−2b)0,40506 c)0,50633.
n≥16
X(Ω) = [|2, n|], p(X > k) = Ck
n
Ak
n
=1
k!, p(X=k) = 1 (k−1)! −1 k!
a)Cn
N, b)Y(Ω) = [|1, N −n+ 1|], c)p(Y≥k) = Cn
N−k+1
Cn
N
, d)p(Y=k) =
Cn−1
N−k
Cn
N
p(X=k) = 2(n−k)
n(n−1) p(Y=k) = 2(k−1) n(n−1).