Two independent darts are thrown uniformly at random at the unit interval [0, 1]. The two darts naturally split the interval into three segments. Let S be the length of the smallest segment. What is E [S]? [Hint: There are several ways to solve this problem. A good way to start is to derive the tail of S, and then integrate the tail to get E [S], as in Exercise 7.9. To get the tail, it may help to draw a 2D picture of where each of the darts is allowed to fall.]