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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 Pólya'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. Tags asymptotic, normality, probability, proof, statistics Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tradermartin92 Advanced Statistics 1 March 22nd, 2016 04:51 AM Scully Advanced Statistics 0 August 27th, 2015 05:09 AM alfred_oh Computer Science 1 May 14th, 2013 12:15 PM ZardoZ Advanced Statistics 1 September 18th, 2011 04:30 PM Apprentice123 Number Theory 1 March 18th, 2009 09:58 AM

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