Central Limit Theorem · Statistics Graduate Level

Statistics Graduate Level Quiz

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CONVERGENCE & LIMIT THEOREMS

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Let

X_1,X_2,\ldots

be independent and identically distributed with

E[X_i]=0

and

\operatorname{Var}(X_i)=1

. Consider the unequally weighted statistic

T_n=n^{-3/2}\sum_{i=1}^n iX_i

. Which limiting distribution follows from an appropriate triangular-array central limit theorem?

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