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May 23rd, 2019, 01:40 PM  #1 
Newbie Joined: May 2019 From: Argentina Posts: 1 Thanks: 0  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 02:41 PM. 

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