Mathematics · Limit Theorems
Let X1, X2, ... be a sequence of independent and identically distributed random variables with E(X1) = 0, E(X12) = 1, E(X13) = 0, E(X14) = 3. Let Sn = Σi=1n Xi, Tn = Σi=1n Xi2, Un = Σi=1n Xi4. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Tn - nn converges in distribution to a random variable Z, where Z ~ N(0, 1)
- 2Un - 3n√n converges in distribution to a random variable Z, where Z ~ N(0,1)
- 3Tn - n√(3n) converges in distribution to a random variable Z, where Z ~ N(0, 1)
- 4Sn√n converges in distribution to a random variable Z, where Z ~ N(0,1)✓
Correct answer
Sn√n converges in distribution to a random variable Z, where Z ~ N(0,1)
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