16 3. Let X₁, X2,..., Xn be random variables with a common mean μ. Sup- pose that cov[X₁, X;] = 0 for all i and j such that j > i + 1. If 2 Q₁ = (X₂ - X)² VECTORS OF RANDOM VARIABLES prove that n and Q2 = (X₁ X₂)² + (X2 − X3)² + + (Xn−1 − Xn)² + (Xn − X₁)², i=1 [3Q₁ Q₂] E 3² = var[X]. n(n − 3) -

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