Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/12/84; site aero.ARPA Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!decwrl!Glacier!oliveb!hplabs!sdcrdcf!trwrb!aero!sinclair From: sinclair@aero.ARPA (William S. Sinclair) Newsgroups: net.math Subject: Probability Problem; Reward! Message-ID: <523@aero.ARPA> Date: Wed, 30-Oct-85 19:38:43 EST Article-I.D.: aero.523 Posted: Wed Oct 30 19:38:43 1985 Date-Received: Sun, 3-Nov-85 08:57:35 EST Reply-To: sinclair@aero.UUCP (William S. Sinclair) Organization: The Aerospace Corp., El Segundo, CA Lines: 19 I will send $20 to the first person who gives an analytic solution to this problem: Suppose we pick n points from a uniform distribution in two dimensions, for example (0,1) in both x and y. Now form the convex hull of these. k of these points will be inside the convex hull, while n-k will be ON the hull. What is the formula for P(n,k), the probability that exactly k points out of n will be inside? Hint (1): p(3,3)=1.0 Hint (2): As n gets large, the expected value of k grows as sqrt(n). I will check your formula by using a Monte Carlo simulation. Bill S. Go ahead and flame! I brought marshmallows!! 213/647-1753