单位正方形的边上均匀随机取三点，其所构成三角形的面积期望

Nicolas2050

Problem_1

Three points are chosen at random (uniformly) from the boundary of a unit square. What is the expected value of the area of the triangle they form?
单位正方形的边上均匀随机取三点，其所构成三角形的面积期望；

Problem_2

Four points are chosen at random (uniformly) from the boundary of a unit cube. What is the expected value of the volume of the tetrahedron they form?

单位正方体的12条边上均匀随机取4点，其所构成四面体的体积期望；