e*******t
发帖数: 111 | 1 地板上画满了间隔一寸的平行线。一根一寸长的牙签随机落到地板上，问牙签压上其中
一条线的几率是多少？ |
s**x
发帖数: 405 | |
r**h
发帖数: 1288 | 3 http://en.wikipedia.org/wiki/Buffon%27s_needle
【在 e*******t 的大作中提到】
: 地板上画满了间隔一寸的平行线。一根一寸长的牙签随机落到地板上，问牙签压上其中
: 一条线的几率是多少？
|
z****p
发帖数: 18 | 4
2/pi
【在 e*******t 的大作中提到】
: 地板上画满了间隔一寸的平行线。一根一寸长的牙签随机落到地板上，问牙签压上其中
: 一条线的几率是多少？
|
z****p
发帖数: 18 | 5
1. consider the case that the stick forms an angle beween 0 and 90 degree (0
to pi/2)
--the angle distribution is uniformly between 0 and pi/2 (with pdf of 2/pi)
--the other cases will be symmetric and so give the same answer
2. convince yourself that the probability of overlapping a line is the same
as the length of the projection of the stick on the x-axis
3. the expected length of projection on the x-axis is:
--integration t from 0 to pi/2 of 2/pi*cos(t)
--the above integration gives 2/pi
【在 z****p 的大作中提到】
:
: 2/pi
|
e*******t
发帖数: 111 | 6 多谢解释！
上面三位都是牛人啊。看来我要学的东西很多。
0
same
【在 z****p 的大作中提到】
:
: 1. consider the case that the stick forms an angle beween 0 and 90 degree (0
: to pi/2)
: --the angle distribution is uniformly between 0 and pi/2 (with pdf of 2/pi)
: --the other cases will be symmetric and so give the same answer
: 2. convince yourself that the probability of overlapping a line is the same
: as the length of the projection of the stick on the x-axis
: 3. the expected length of projection on the x-axis is:
: --integration t from 0 to pi/2 of 2/pi*cos(t)
: --the above integration gives 2/pi
|
j******2
发帖数: 362 | |
e*******t
发帖数: 111 | 8 A
【在 j******2 的大作中提到】
: 请问这是哪家的题？
|
