on internet I found something like:
var(XY)=Var(X)var(Y)+var(X)E[Y]^2+var(Y)E[X]^2
but there is the assumption of Yand X independent, that is hardly my case.
Probably I am complicating too much the question, so I give you the equation I have to solve, because probably there is an easier solution:
E[-e^-alpha(Y+Z)^2] that is:
-e^-alpha[E[Y+Z]^2-alpha/2*var[(Y+Z)^2] with Y and Z distributed as normal
thank you