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From: apdoo@alice.UUCP (Alan Weiss)
Newsgroups: net.math
Subject: Re: Yet another probability puzzle
Message-ID: <2619@alice.UUCP>
Date: Mon, 27-Feb-84 13:41:26 EST
Article-I.D.: alice.2619
Posted: Mon Feb 27 13:41:26 1984
Date-Received: Tue, 28-Feb-84 08:26:51 EST
References: <703@ihuxq.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 20


	There are at least two ways of solving this problem, which I shall
now give.  The problem was to find the mean range of n numbers chosen
uniformly on the interval (0,1).
1. Easy solution
	Write u for the value of the maximum, l for the value of the minimum.
Then range=u-l, and
E(range)=E(u-l)=E(u)-E(l)=1-1/(n+1) -1/(n+1) = 1-2/(n+1) .
2. Harder solution, which gives more information.
	Suppose we ask the question "What is the DISTRIBUTION of the range?".
Then we find for any number t in the range (0,1)
P(range