Probabilités 5 − LICENCE L3

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XN(0,1)
∀x∈R, fX(x) = 1
√2πexp −x2
2σ2.
XN(0,1)
Y=aX +b a, b ∈Ra6= 0
E[Xn]n≥1 (X)
FXX FX(−t)FX(t)
t∈R
Z=X2+ 2X Z
X Y N(0,1)
T=Y/X
ρ=√X2+Y2θ= arctan(Y/X) (ρ, θ)
Y/X θ
X+Y X −Y
W1/2V[0; 2π]
W X =√Wcos(V)Y=√Wsin(V)X Y
N(0,1)
λ > 0fR2R
∀(x, y)∈R2, f(x, y) = λ4
2x2exp(−λy)1{0<x<y}.
f
(X, Y )f
X Y