3 For an integer n 1, let X1, X2, , Xn be identically distributed random variables with Var(Xi) 2, 1 i n For i, j, 1 i 6 j n, let (Xi,Xj) a, for a constant a Show that a 1 n 1 Hint Start with Var(X1 X2 Xn) 0

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Question: 3. For an integer n > 1, let X1, X2, . . . , Xn be identically distributed random variables with Var(Xi) = 2, 1

3. For an integer n > 1, let X1, X2, . . . , Xn be identically distributed random variables with Var(Xi) = σ2, 1 ≤ i ≤ n. For i, j, 1 ≤ i 6= j ≤ n, let ρ(Xi,Xj) =

a, for a constant

a. Show that a ≥ −

1 n − 1

Hint: Start with Var(X1 + X2 + · · · + Xn) ≥ 0.

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