Mathematics · Probability Theory
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 = ∑ Xi, Tn = ∑ Xi2, Un = ∑ Xi3 and Vn = ∑ Xi4 (all sums from i=1 to n). Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Sn / √n converges in distribution to a random variable Z, where Z ~ N(0, 1)
- 2(Tn - n) / √(3n) converges in distribution to a random variable Z, where Z ~ N(0, 1)
- 3(√n Sn) / Tn converges in distribution to a random variable Z, where Z ~ N(0, 1)
- 4(Tn - n) / √Vn converges in distribution to a random variable Z, where Z ~ N(0, 1)✓
Correct answer
(Tn - n) / √Vn converges in distribution to a random variable Z, where Z ~ N(0, 1)
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