PHQ057 Techniques expérimentales

x
x x
E(x) = X
i
p(xi)xi
E(x) = ˆxP (x) dx
x
V(x) = X
i
p(xi)(xi−x)2
V(x) = ˆ(x−x)2P(x) dx
σ σ(x) = pV(x)σ
x x σ =E[(x−x)2]
x y cov(x, y)
cov(x, y) = ¨(x−x)(y−y)P(x, y) dxdy
x y
y=ax +b x y
x
p N
P(x/N) = N!
x!(N−x)!px(1 −p)N−x
σx2=Np(1 −p)
x=Np
N1p1
P(x) = xxe−x
x!
σx2=Np
x=Np
p1 (1 −p)∼1
x x &10
P(x) = 1
σ√2πe−(x−x)2
2σ2

∆x σx
∆x= 2√2 ln 2σx'2,35σx
x
x10 x
x1√x'√x
x∈[x−σ;x+σ]≡68,3%
x∈[x−2σ;x+ 2σ]≡95,5%
x∈[x−3σ;x+ 3σ]≡99,7%
x x
x±σxy±σyu=f(x, y)u
σu
σu2=σx2∂f
∂x 2
+σy2∂f
∂y 2
+ 2 cov(x, y)∂2f
∂x∂y
x y cov(x, y) = 0
σu=sσx2∂f
∂x 2
+σy2∂f
∂y 2
∆u= ∆x∂ f
∂x + ∆y
∂ f
∂y 
NE
NB
Ns=NE−NB
L Ns< L
L
NsNs=Ns= 0

NB±pNB
NE±pNE
Ns
σs=pNB+NE'√2pNB
NE∼NB
P(Ns< L)=0,95
x→x−x
σ
P(t) = 1
√2πexp −t2
2
t=x−x
σx σ
x−
70
x
σs
61,645
L= 1,645√2pNB
L= 2,326σNB
L x 95%
L
P(Ns> L)=0,95
P(Ns−Ns
σs
>L−Ns
σs
)=0,95
L−Ns
σs
= 1,645
Ns= 1,645σs+L
Ns= 4,653σNB
NE∼NB
EdE
∆E
N
R
R=∆E
E