Let Xn be a sequence of independent and uniformly bounded random variables, and E[Xn]=0, and Var(Xn)=dfrac12n for each n. Let Sn=X1+dots+Xn and sigman^2=Var(Sn). Then which of the following is not true?

(A) Sn/sigman does not converge in distribution

Q137Section III (Statistics)137 of 190

Uniform boundedness with diverging total variance forces the CLT via Lyapunov's condition

Let $\{X_n\}$ be a sequence of independent and uniformly bounded random variables, and $E[X_n]=0$ , and $\operatorname{Var}(X_n)=\dfrac1{2n}$ for each $n$ . Let $S_n=X_1+\dots+X_n$ and $\sigma_n^2=\operatorname{Var}(S_n)$ . Then which of the following is not true?

Pick an option to check your answer.

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