  Let a random simplex in a d-dimensional convex body be the convex hull of d+1
random points from the body. We study the following question: As a function of
the convex body, is the expected volume of a random simplex monotone
non-decreasing under inclusion? We show that this holds if d is 1 or 2, and
does not hold if d >= 4. We also prove similar results for higher moments of
the volume of a random simplex, in particular for the second moment, which
corresponds to the determinant of the covariance matrix of the convex body.
These questions are motivated by the slicing conjecture.
