# $X_i = i^{\delta}Z_i$, find the range of $\delta$ for which the law of large numbers and the central limit theorem are valid

$$Z_1,Z_2,...$$ are i.i.d., their expected value is zero, their variance $$\sigma^2$$, and $$E[|Z_i^2|] = m_3 < \infty$$. $$X_i = i^{\delta}Z_i$$, find the range of $$\delta$$ for which the law of large numbers and the central limit theorem are valid.

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