My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
May 23rd, 2019, 01:40 PM   #1
Joined: May 2019
From: Argentina

Posts: 1
Thanks: 0

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 02:41 PM.
alaanmdq is offline  

  My Math Forum > High School Math Forum > Probability and Statistics

asymptotic, normality, probability, proof, statistics

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Which test for normality is the most appropriate? tradermartin92 Advanced Statistics 1 March 22nd, 2016 04:51 AM
Normality Scully Advanced Statistics 0 August 27th, 2015 05:09 AM
Explanation of the proof of a lemma of Asymptotic analysis alfred_oh Computer Science 1 May 14th, 2013 12:15 PM
Normality Limit! ZardoZ Advanced Statistics 1 September 18th, 2011 04:30 PM
Asymptotic analysis Apprentice123 Number Theory 1 March 18th, 2009 09:58 AM

Copyright © 2019 My Math Forum. All rights reserved.