Mathematics · Probability Theory
Let {X n } n≥1 be a sequence of independent and identically distributed random variables with E(X 1 ) = 0 and Var(X 1 ) = 1. Which of the following statements is NOT true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1lim n→∞ P(∑ i=1 n X i ≤ 0) = 1 2
- 2The sequence ∑ i=1 n X i √n converges in probability to 0 as n → ∞✓
- 3The sequence ∑ i=1 n X i ∑ i=1 n X i 2 converges in probability to 0 as n → ∞
- 41 n ∑ i=1 n X i 2 converges in probability to 1 as n → ∞
Correct answer
The sequence ∑ i=1 n X i √n converges in probability to 0 as n → ∞
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