Mathematics · Limit Theorems in Probability
Let X1, X2, ... be a sequence of independent and identically distributed random variables with E(X1) = 0, E(X12) = 1, E(X13) = 0, and E(X14) = 3. Let Sn = ∑i=1n Xi, Tn = ∑i=1n Xi2, Un = ∑i=1n Xi3, and Vn = ∑i=1n Xi4. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(Tn - n)/√Vn converges in distribution to a random variable Z, where Z ~ N(0,1)
- 2(√n × Sn)/Tn converges in distribution to a random variable Z, where Z ~ N(0,1)
- 3(Tn - 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)✓
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Sn/√n converges in distribution to a random variable Z, where Z ~ N(0,1)
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