[net.math] Probability Problem; Reward!

sinclair@aero.ARPA (William S. Sinclair) (10/31/85)

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