Somme de variables aléatoires indépendantes

Somme de variables aléatoires indépendantes

\(P_{X+Y}(A)=\) \(\int_{{\Bbb R}^d}\int_{{\Bbb R}^d}\Bbb 1_{x+y\in A}\,dP_X(x)\,dP_Y(y)\)
on note \(P_{X+Y}=P_X\star P_Y\)
\(P_{X+Y}=\) \((f_X*f_Y)\lambda_d\)
\(\phi_{X+Y}=\) \(\phi_X\phi_Y\)
si \(X,Y\) \(\in L^2\), alors \(V(X+Y)=V(X)+V(Y)\)

Math'φsics