D12M - Le parc

π
f
[0,1] I=Z1
0
f(t) dt
X[0,1] Y=f(X)
Y E(Y) = I Y
σ2
f
Y
(Yk)Y
Mn=1
n
n
X
k=1
Yk
Sn=v
u
u
t
1
n
n
X
k=1
(Yk−Mn)2
Mn, Snn95%
I
π
Z1
0
4√1−x2dx=π
f(x) = 4√1−x2
n π
95%
n= 10kk∈ {2,3,4,5,6,7}
π
f
Z=1
2f(X) + f(1 −X)
1−X
E(Z) = π
g(x) = 1
2f(x)+f(1−x)
n
f g
g f Y Z

J=Z+∞
0
e−x3dx
J
λ > 0X λ
hλE(hλ(X)) = J hλ(X)
lam
lam
λ= 1 n= 10 000 000
hλ(X)J0.95%
λ
n= 10 000
λ λ 0.5 5
λ0.1
λ J n =
10 000 000
J
J
10 000
n= 1000 λ
J