  The oloid is the convex hull of two circles with equal radius in
perpendicular planes so that the center of each circle lies on the other
circle. We calculate the mean width of the oloid in two ways, first via the
integral of mean curvature, and then directly. Using this result, the surface
area and the volume of the parallel body are obtained. Furthermore, we derive
the expectations of the mean width, the surface area and the volume of the
intersections of a fixed oloid and a moving ball, as well as of a fixed and a
moving oloid.
