Test Your intuition 51

Combinatorics and more 2022-10-11

Suppose that K and L are two compact convex sets in space. Suppose that K contains L. Now consider two quantities

  • X is the average volume of a simplex forms by four points in K drawn uniformly at random.
  • Y is the average volume of a simplex forms by four points in L drawn uniformly at random.

TYI: Is it always the case that X ≥ Y?