Let W be an m × 1 vector with covariance matrix ∑W, where ∑W is finite and positive definite. Let c be a nonrandom m × 1 vector, and let Q = c′W.
a. Show that var(Q) = c′∑Wc.
b. Suppose that c ≠ 0m. Show that 0 < var(Q) < ∞.