**12. Correct. The answer is false.**

You can deduce the formula of X + Y as follows:

Var [X+Y] = E [ (X+Y)
- E(X+Y) ]^{2}

Squarin the binomial, you get:

Var [X+Y] = E{[X - E(X)^{2}}
+ E{[Y - E(Y)^{2}} + 2 E {[X - E(X)] [Y - E(Y)] }

Applying the definitions of variance and covariance to the right-hand side, the variance of the sum becomes:

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

Using the numbers with this formula, you have:

Var [X+Y] = 50 + 20 + 2*(-27) = 16

The standard deviation of the
portfolio is: {Var[X+Y]}^{0.5}
= US$ 4.