Hey MartinDalskov.

For these expressions, there is a well known one for variance and with two variables we have:

Var[X+Y] = Var[X] + Var[Y] + 2*Cov(X,Y) with

Var[aX] = a^2*Var[X] and

Var[X+c] = Var[X] for some constant c.

If X and Y are independent then Cov(X,Y) = 0 but if not you must include this term.