The Volume of a Tetrahedron whose Vertices are Chosen at Random in the Interior of a Parent Tetrahedron

We solve a problem proposed by V. Klee (1969). He asked for a calculation of ., the expected value of V, the volume of a daughter tetrahedron whose vertices are chosen at random (i.e. independently and uniformly) in the interior of a parent tetrahedron of unit volume. We discover: https://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aartic le%3AS0001867800026434/resource/name/S0001867800026434_eqn1.gif?pub-stat us=live We also calculate the second, fourth and sixth moments of V.