  We analyze the correctness of an O(n log n) time divide-and-conquer algorithm
for the convex hull problem when each input point is a location determined by a
normal distribution. We show that the algorithm finds the convex hull of such
probabilistic points to precision within some expected correctness determined
by a user-given confidence value. In order to precisely explain how correct the
resulting structure is, we introduce a new certificate error model for
calculating and understanding approximate geometric error based on the
fundamental properties of a geometric structure. We show that this new error
model implies correctness under a robust statistical error model, in which each
point lies within the hull with probability at least that of the user-given
confidence value, for the convex hull problem.
