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 December 13th, 2017, 12:59 PM #1 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Interpretation of Limiting Distribution Let $X_1, ..., X_n$ be random variables independent and identically distributed on $Uniform(0,1)$. Let $X_{(n)}=MAX{(X_1,...,X_2)}$. Define $W_n=n(1-X_{(n)})$. Find the limiting distribution of $W_n$ as $n$ increases without bound. Can you identify this limiting distribution? Give an interpretation of the result obtained above. So, I managed to find that the limiting distribution follows an exponential distribution with mean 1. However, I'm not quite sure how to "interpret" this. What's so special about $W_n$ that makes this result significant when $n$ grows large? December 13th, 2017, 03:56 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,430 Thanks: 1315 I get that $f_{W_{(n)}}(w) = \left(1 - \dfrac w n \right)^{n-1},~w \in [0,n]$ $\lim \limits_{n\to\infty}~f_{W_{(n)}}(w) = e^{-w},~w \in [0,\infty)$ December 13th, 2017, 04:18 PM #3 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Right, that's exactly what I found; it's exponential with mean 1. But the real question here is: how do you "interpret" that? Tags distribution, interpretation, limiting 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 Keroro Advanced Statistics 0 June 14th, 2016 03:29 PM Aqil Advanced Statistics 0 March 9th, 2013 10:13 AM problem Advanced Statistics 1 November 2nd, 2009 01:36 PM illusion Advanced Statistics 0 December 4th, 2007 11:32 AM illusion Advanced Statistics 0 December 4th, 2007 11:28 AM

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