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May 23rd, 2019, 12:40 PM   #1
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Question Asymptotic Normality proof

I'd like some assistance on the proof of the following Lemma:
If $X_n$ is $AN(\mu,\sigma_n^2)$, then also $X_n$ is $AN(\overline\mu,\overline\sigma_n^2)$ if and only if $\displaystyle \frac{\overline\sigma_n}{\sigma_n}\rightarrow1$, $\displaystyle \frac{\overline\mu_n-\mu_n}{\sigma_n}\rightarrow0$.
The hint says to use PĆ³lya's Theorem, which relates weak convergence and uniform convergence, but I'm not sure about how to use it. Thanks in advance.

Last edited by skipjack; May 23rd, 2019 at 01:41 PM.
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