随机序列的最大连续子之和展望

下面是编程珠玑的问题第2版（第8.7）：

Here is a problem from Programming Pearls 2nd edition (Chapter 8.7):

考虑到一个真正的数字序列，它的元素均匀的范围绘制 [ - 1，1] ，什么是预期的最大连续子之和？ （如果所有的元素都是负值，最大的一笔是 0 ）

Considering a real number sequence, whose elements are drawn uniformly from the range [-1, 1], what is the expected maximum consecutive subsequence sum? (If all the elements are negative, the maximum sum is 0.)

假设序列的长度 N ，是有一个封闭的形式为预期的最大子之和 F（N）？我试着做一些模拟，但未能找到任何线索。

Assuming the length of the sequence is N, is there a closed form for the expected maximum subsequence sum f(N)? I try to do some simulation, but failed to find any clue.

感谢您的帮助。