Mathematics · Probability and Statistics
For n > 1, let X 1 , X 2 , ..., X n be random variables such that E(X i ) = 0 and E(X i 2 ) = 1 for all i, and E(X i X j ) = ρ for all i ≠ j. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Var(X 1 + X 2 + ... + X n ) = n if and only if ρ = 0✓
- 2Var(X 1 + X 2 + ... + X n ) = n if and only if X 1 , X 2 , ..., X n are pairwise independent
- 3Var(X 1 + X 2 + ... + X n ) = n if and only if X 1 , X 2 , ..., X n are independent
- 4ρ = 0 if and only if X 1 , X 2 , ..., X n are independent
Correct answer
Var(X 1 + X 2 + ... + X n ) = n if and only if ρ = 0
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