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From: sarwate@uicsl.UUCP
Newsgroups: net.math
Subject: Re: Re: Yet another probability puzzle - (nf)
Message-ID: <6486@uiucdcs.UUCP>
Date: Fri, 30-Mar-84 23:00:06 EST
Article-I.D.: uiucdcs.6486
Posted: Fri Mar 30 23:00:06 1984
Date-Received: Sat, 31-Mar-84 09:56:41 EST
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#R:tekchips:-59000:uicsl:6900005:000:323
uicsl!sarwate    Mar 30 10:26:00 1984


Your answer for h sub N (y) is right as is the expected value.  See e.g.
Michael Woodroofe "Probability with Applications", McGraw-Hill 1975.
The density of the range is computed on page 190.  This is a beta density
with parameters alpha = N-1 and beta = 2.  The expected value is given
as alpha/(alpha+beta) on page 218.