TD N°3 Probabilité-Statistique

P(X= 1) = p p ∈R0≤p≤1
k∈N∗)
x1;x2;..........;xn
p1;p2;..........;pnpi=P(X=xi)
Y=aX +b
E(Y) = aE(X) + b
V(Y) = a2V(X)
x∈Rf(x)
∀x∈R, P (X≤x) = F(x) = ∫x
−∞
f(t)dt
Y=aX +b
E(Y) = aE(X) + b
V(Y) = a2V(X)
V(x) = E(X2)−[E(X)]2
[a, b] (a < b)R
[a, b]
∀x, f(x) = c
1 + x2, where c ∈R

x=rcos θ y =rsin θ
dxdy =rdrdθ
I1=∫+∞
−∞
e−x2/2dx
I2=1
σ√2π∫+∞
−∞
e−1/2( x−m
σ)2dx = 1