12. Incorrect. The answer is false, not true.

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

Var [X+Y] = E [(X+Y) - E(X+Y) ]²

Squaring 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.