Lois de probabilité continues (1)

y y
−
X λ = 8
P(0 < X < 7)
P(0 < X < 7) = 1 −e−56
P(0 < X < 7) = −e−56
P(0 < X < 7) = e−56
P(0 < X < 7)
X λ = 4
P(0 < X < 9)
P(0 < X < 9) = 1 −e−36
P(0 < X < 9) = −e−36
P(0 < X < 9) = e−36
P(0 < X < 9)
X λ = 2
E(X)
E(X) = 1
2E(X)=2 E(X) = e2
E(X)
y y

y y
X[−1 ; 6]
P(1 < X < 3)
P(1 < X < 3) = 2
7
P(1 < X < 3) = 1
7
P(1 < X < 3) = 2
P(1 < X < 3)
k x →k·x2
k=3
54
k=54
3
k=1
3
k
k x →k·x2
k=3
72
k=72
3
k=1
3
k
y y

y y
X λ
P(0 < X < 5) = 0,02 λ
λ=−ln(0,98)
5
λ=−ln(0,02)
5
λ=ln(0,02)
5
λ
X λ
P(0 < X < 6) = 0,18 λ
λ=−ln(0,82)
6
λ=−ln(0,18)
6
λ=ln(0,18)
6
λ
X λ = 46
E(X)
E(X) = 1
46 E(X) = 46 E(X) = e46
E(X)
X λ = 6
P(0 < X < 8)
P(0 < X < 8) = 1 −e−48
P(0 < X < 8) = −e−48
P(0 < X < 8) = e−48
P(0 < X < 8)
y y

y y
k x →k·x2
k=3
65
k=65
3
k=1
3
k
X λ = 40
E(X)
E(X) = 1
40 E(X) = 40 E(X) = e40
E(X)
X[−5 ; 2]
P(−3< X < 0)
P(−3< X < 0) = 3
7
P(−3< X < 0) = 1
7
P(−3< X < 0) = 3
P(−3< X < 0)
X[−3 ; 7]
P(−2< X < 4)
P(−2< X < 4) = 6
10
P(−2< X < 4) = 1
10
P(−2< X < 4) = 6
P(−2< X < 4)
y y

y y
X λ
P(0 < X < 7) = 0,72 λ
λ=−ln(0,28)
7
λ=−ln(0,72)
7
λ=ln(0,72)
7
λ
y y