       • To: mathgroup at smc.vnet.net
• Subject: [mg57052] Integrate gives wrong answer
• From: "Brian Rogers" <brifry at gmail.com>
• Date: Thu, 12 May 2005 22:44:45 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi, I have a problem on which Integrate misses badly. The code consits
of:

fmin[x_, p_]:=[p(1-(x-a+e)/(2e))^(p-1)]/2e

which is the pdf of the minimum of p draws from a uniform distribution
on [a-e,a+e], and

Integrate[Abs[Min[mi,mc]-Min[mj,mc]]*fmin[mc,k]*fmin[mi,ni-k]*fmin[mj,nj-k],
{mc,a-e,a+e},{mi,a-e,a+e},{mj,a-e,a+e},Assumptions->{k\el\_Integers,
ni\el\_Integers,nj\el\_Integers,1<=k<=Min[ni,nj],0<a-e<a+e<1}]

This produces the output:

\!\(k\ \((\(a +
e\)\/ni - \(2\ e\)\/\(1 + ni\) + \(a + e\)\/\(k - ni - nj\) +
\(2\ \
e\)\/\(1 - k + ni + nj\))\)\)

which is not symmetric betwenn ni and nj, as it should be.

Any ideas?
Thanks!
Brian Rogers
brifry at gmail.com

```

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