Mathematics · Probability Theory
Let (X n , n ≥ 1) be independent and identically distributed (i.i.d.) random variables with mean zero and variance one. Which of the following statements is NOT true as n → ∞?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1X 1 + X 2 + ... + X n n + 1 converges to zero in probability
- 2X 1 - X 2 + ... + (-1) n+1 X n √n converges in distribution to a standard normal distribution
- 3X 1 + X 2 + ... + X n √n converges to zero in probability✓
- 4X 1 + X 2 + ... + X n √n+1 converges in distribution to a standard normal distribution
Correct answer
X 1 + X 2 + ... + X n √n converges to zero in probability
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