UE Statistique, rappels, 2014-2015

57% 63% 71% 80% 90%
J N N =JCV B
V=BC
P(J) = .25 P(N) = .75
P(V) = .80 P(B) = .2
P(J|B) = .1

P(N|V)
P(J|B) = P(J∩B)
P(B)=.1P(J∩B) = .1×.2
P(N|V) = P(N∩V)
P(V)=P(V)−P(NC∩V) P(V)
P(NC∩V) = P(NC)−P(NC∩VC) = P(J)−P(J∩B)
P(N|V) = P(V)−[P(J)−P(J∩B)]
P(V)
P(N|V) = .8−[.25 −.02]
.8=.7125
A B C D E vide
Question 1
0 20 40 60 80 100
correct 45%

0.223 0.777 0.198 0.961 0.5
N N
n= 100 p= 1/30
P(N= 3) = n
3p3(1 −p)n−3=100! 97!3!
|{z}
100×99×98/2×3
1
303
2997
3097∼0.2234551
A B C D E vide
Question 2
0 20 40 60 80 100
correct 70%
1
216
1
36
3
216
4
9
1
8

1 6
1 36
A B C D E vide
Question 3
0 20 40 60 80 100
correct 50%
X Y
X
Y1/12 1/6
1/18 1/3
P(X≤2)
1
12
1
2
5
36
2
3
1
3

X≤2
1
12 +1 18 +1 6+13 36 =3+2+6+13 36 =24 36 =2 3
A B C D E vide
Question 4
0 20 40 60 80 100
correct 85%
X
[−2,2] X > 1X≤2
0.347 0.452 0.244 0.628 0.549
P(X≤2|X > 1) = P({X≤2}∩{X > 1})
P(X > 1) =P(X∈[1,2]) P(X > 1)
P(X≤2|X > 1) = P(log(X)∈[log(1),log(2)])
P(log(X)>log(1)) =P(log(X)∈[0,log(2)]) P(log(X)>0)
log(X) [−2,2]
P(log(X)>0) = 2−0
2− −2=2 4=1 2