Statistiques en L1 Sociologie et Psychologie

α β γ δ  ζ θ λ µ ξ ρ σ φ ψ ω
Γ ∆ Λ Ξ Σ Φ Ψ Ω χ
Px
xPx

x y a 6= 0 b c 6= 0 d
m(ax +b) = am(x) + b
σ(ax +b) = aσ(x)
cov(ax +b, cy +d) = ac ·cov(x, y)
r(ax +b, cy +d) = r(x, y)
95,97,100,103,105 100
5
Z=x−100
5Z
x
x µxσxz=x−µx
σx
0 1
1
nX
j yjX i
nij xi!(1
nX
i
xiX
j
nij yj
).
5
Ω Ω (i, j)i j
1 6
Ω
ω P ({ω})ω
P({ω}) = 1
36.
P(A) = A
Ω.
X(i, j) = i+j.
P(X= 2) P(X= 12) P(X= 3)
P(X= 3) = (i, j)i+j= 3
36 .
N N1N2n
X
n
n≤N n

P(x=k) = n
kN1
NkN−N1 Nn−k
.
p=N1
N
P(x=k) = n
kpk(1 −p)n−k.
X=B(n;p)
p q = 1 −p
P(X= 0) = 1 −p
P(X= 1) = p X
(1 −p)×0 + p×1 = p.
p−p2=pq
X4
X
1
16 ×0 + 4 16 ×1 + 6 16 ×2 + 4 16 ×3 + 1 16 ×4=2=4×1 2.
1
16 ×(0 −2)2+4 16 ×(1 −2)2+6 16 ×(2 −2)2+4 16 ×(3 −2)2+1 16 ×(4 −2)2= 1.
np npq
X=B(n;p)µ=np, V =npq.
P(X=k) =
N1
k N−N1 n−k
N
n0≤k≤N1,0≤n−k≤N−N1
0.
X=H(N;N1;n)p=N1
N
µ=np, V =np(1 −p)N−n
N−1.
n≥30 np > 5nq > 5X=B(n;p)np √npq
X=H(N;N1;n)np
√npqqN−n
N−1

90
4.38 0.08
0.95 0.99 [4.363; 4.397]
[4.358; 4.402]