Suppose X & Y are two independent stocks' returns with:

Question

E(X) = E(Y) =15% and V(X) = 144,
V(Y) = 256

Problem 1. Buy half X and half Y, so
w1 = w2 = 0.5 and Z = (X+Y)/2

Note: The answer says that the variance is 100 but I thought it would be 200. Since I would be adding half each of the variances of X & Y. Thus getting X=72 and Y=128 or 200.

Why is it 100? I am confused.