Some important identities:

Var(aX-b) = a^2 Var(X)

Var(X1 + X2) = Var(X1) + Var(X2) + 2*Covar(X1,X2)

Covar(X,aX) = a*Var(X)

If we assume no lag autocorrelation exists in your signal then Covar(X,X(x-b))=0

Thence Var(F3) = Var(F1) + Var(F2) + 2*Covar(F1,F2)

                       = Var(F1) + a^2*Var(F1) +  0

                       = (1+a^2) * Var(F1)

My Dear 

var(x1+x2)=var(x1)+var(x2)+(-)cov(x1,x2)

and answer Mr. Kieran Hunt is very good about subject 

Thank you for your answers, they are very interesting.