Let X1, X2, ..., Xn be random variables whose marginal distributions are N(0, 1). Suppose E(XiXj) = 0 for all i ≠ j. Let Y = X1 + X2 + ... + Xn. Which of the following statements is always true?

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Mathematics · Mathematical Statistics

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Y has a normal distribution with mean zero and variance n

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Answer 1

P(|Y| > t) ≤ nt2 for all t > 0

Answer 2

E(Xi3Xj3) = 0 for all i ≠ j

Answer 3

V = ∑Xi2 has a Chi-square distribution with n degrees of freedom

Answer 4

Y has a normal distribution with mean zero and variance n

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