2. For random variables X1, X2, . . . , Xn, we have that Var(Xi) = 4, 1 ≤ i ≤ n, and for 1 ≤ i 6= j ≤ n, ρ(Xi,Xj) = −1/16. Find Var(X1 + X2 + · · · + Xn).

Hint: Note that Pn−1 i=1 Pn j=i+1 Cov(Xi,Xj) has (n − 1) + (n − 2) + · · · + 1 =

[(n − 1)n]/2 terms.