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From: sinclair@aero.ARPA (William S. Sinclair)
Newsgroups: net.math
Subject: Probability Problem (reward!)
Message-ID: <511@aero.ARPA>
Date: Wed, 23-Oct-85 18:04:10 EST
Article-I.D.: aero.511
Posted: Wed Oct 23 18:04:10 1985
Date-Received: Mon, 28-Oct-85 04:13:53 EST
Reply-To: sinclair@aero.UUCP (William S. Sinclair)
Organization: The Aerospace Corp., El Segundo, CA
Lines: 17


I will send $20.00 to the first person to give the answer.  The problem is:
We select n points from a 2-dimensional uniform distribution, say {0 to 1}
in both x and y. Now we form the convex hull of these, and it will contain
k of the points. What is the probability that k of the n points will be on
the convex hull?

Hint: if n=3, p(k,n)=1.0
Also, as n goes to infinity, the expected value for k goes up like sqrt(n).

Bill S.
Go ahead and flame! I brought marshmallows!!
213/647-1753

P. S. The answers will be checked by a Monte Carlo simulation. You must include
the dervation of your formula.