w******h
发帖数: 9 | 1 This might be an old one, but I cannot figure it out, nor can I find the
answer anywhere.
Given a circle, make n random cuts, what is expected length of longest piece
? |
o******e
发帖数: 1001 | 2 这个不能算是brain teaser了,需要很复杂的计算的. |
t*****a
发帖数: 90 | 3 what exactly do you mean by "random"?
is it the same as a unit length straight line with n-1 independent cuts with
join uniform distribution? |
w******h
发帖数: 9 | 4 I don't really know how to specify it in more detail, as that's all that I
have. We can try to solve however we can restate the problem to clarify it
without losing generality. |
n****y
发帖数: 28 | |
f********y
发帖数: 278 | |
c**********e
发帖数: 2007 | 7 For small n, just calculate the integral. For large n,
use simulations. |
w******h
发帖数: 9 | 8 careerchange, how would you do integral for small n?
Can the integration be extended to larger n? |
|
S*********g
发帖数: 5298 | 9 It is not hard to derive an exact formula for a general n.
【在 w******h 的大作中提到】
: careerchange, how would you do integral for small n?
: Can the integration be extended to larger n?
|
w******h
发帖数: 9 | 10 SuperString, would you mind sharing the answer here?
Thanks |
w******h
发帖数: 9 | 11 SuperString, would you mind sharing the answer here?
Thanks |
l******n
发帖数: 9344 | 12 it is a integral
for n=2, it is .75
higher dimension may be tedious
【在 w******h 的大作中提到】
: SuperString, would you mind sharing the answer here?
: Thanks
|
l******n
发帖数: 9344 | 13 似乎n=3,也是。75
P(x1
-x^2/2+x-1/2 if x\in(1/2,1)
【在 l******n 的大作中提到】
: it is a integral
: for n=2, it is .75
: higher dimension may be tedious
|
