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!ittatc!dcdwest!sdcsvax!sdcrdcf!trwrb!trwrba!aero!sinclair 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.