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Let $Z_i(\theta)=e^{X_i \theta-\frac{1}{2}\theta^2}-1$. Is $\sum Z_i(\theta)=O_p(\sqrt(n))$, $\sum Z^2_i(\theta)=O_p(1)$ and $\sum Z^3_i(\theta)=O_p(1)$ and why?

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