假设我有一个单位长度的线段，我往上随机丢n-1个点，分成n段。应该怎么计算【最长的】那一段的期望长度？

mean_of_longest_segment.py

"""
CuGBabyBeaR @ 2015-2-25

result:

2     0.751132
3     0.611519
4     0.520260
5     0.457999
6     0.407207
7     0.371987
8     0.338186
9     0.314609
10    0.293323
11    0.273639
12    0.256827
dtype: float64
[Finished in 1.1s]
"""

import random as r
import pandas as pd
import numpy as np

def longest(n):
    node = []
    for i in xrange(n-1):
        node.append(r.random())
    node.sort()
    longest = 0
    last = 0
    for x in node:
        if longest < x-last:
            longest = x-last
        last = x
        pass
    if longest < 1-last:
        longest = 1-last
    return longest

def dataset(n, count = 10000):
    res = []
    for x in xrange(count):
        res.append(longest(n))
    return res


def ana(frm = 2, to = 12, count = 10000):
    d = {};
    index = range(10000)
    for x in xrange(frm, to + 1):
        d[x] = pd.Series(dataset(x, count), index = index)
        pass
    df = pd.DataFrame(d)

    print df.mean()

ana()