v********w
发帖数: 136 | 1 a loop of string with unit length. Take n cut independently and randomly,
what is the expected length of the largest piece? |
f*******g
发帖数: 79 | 2 I used the integral and it look like (3/4)^(n-1)?
randomly,
【在 v********w 的大作中提到】
: a loop of string with unit length. Take n cut independently and randomly,
: what is the expected length of the largest piece?
|
v********w
发帖数: 136 | 3 好像不对啊，我做了simulation，不是指数衰减的，接近power law
说说思路把，大家可以讨论讨论
【在 f*******g 的大作中提到】
: I used the integral and it look like (3/4)^(n-1)?
:
: randomly,
|
f*******g
发帖数: 79 | 4 the answer for n=2 case is the integral
int_0^(1/2) 2(1-x)dx.
for general n, it is a n-1 multiple integral. when we reduce the integral
from n to n-1, we get a factor 3/4. |
f*******g
发帖数: 79 | 5 算积分的时候算错了， 试一下这个答案：
（3/4）×（5/6）×...*(2n-3/2n-2)
【在 v********w 的大作中提到】
: 好像不对啊，我做了simulation，不是指数衰减的，接近power law
: 说说思路把，大家可以讨论讨论
|
i**h
发帖数: 17 | 6 http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/January2006.html
【在 v********w 的大作中提到】
: a loop of string with unit length. Take n cut independently and randomly,
: what is the expected length of the largest piece?
|
v********w
发帖数: 136 | |
t*******y
发帖数: 637 | |
