w******g
发帖数: 67 | 1 【 以下文字转载自 JobHunting 讨论区 】
发信人: wyizhang (MM>美眉，MM=我的宝贝儿), 信区: JobHunting
标 题: 问道 面试题
发信站: BBS 未名空间站 (Wed Aug 18 20:54:55 2010, 美东)
Line segment between 0 and 1. Choose two points randomly on the line. What
is the average distance between them?
没有思路，谁给点提示或者参考，多谢。 | n****e
发帖数: 629 | 2 假设期望是x
把0--1分成两部分：0--0.5--1
50%可能两点落在0.5的同一边 50%可能两点落在两边
落在一边的话 期望是x/2 落在两边的话 期望是1/2
therefore, x = 1/2*(x/2) + 1/2*(1/2)
x = 1/3
【在 w******g 的大作中提到】
: 【 以下文字转载自 JobHunting 讨论区 】
: 发信人: wyizhang (MM>美眉，MM=我的宝贝儿), 信区: JobHunting
: 标 题: 问道 面试题
: 发信站: BBS 未名空间站 (Wed Aug 18 20:54:55 2010, 美东)
: Line segment between 0 and 1. Choose two points randomly on the line. What
: is the average distance between them?
: 没有思路，谁给点提示或者参考，多谢。
| f***a
发帖数: 329 | 3 More generic solution:
U~f(u),V~f(v), and X=U-V.
You want to find distribution of X.
Simply let Y=V.
since U,V are indedendent => f(u,v)=f(u)f(v)
=> g(x,y)=f(u(x,y),v(x,y))*|J(x,y)|, where J(x,y) is Jacobian transformation
matrix.
=> g(x)= /int g(x,y) dy
from here, you should have no problem to find the answer. | l******f
发帖数: 568 | 4 double integral
btw, which type of business you interviewed? IT? stat?
【在 w******g 的大作中提到】
: 【 以下文字转载自 JobHunting 讨论区 】
: 发信人: wyizhang (MM>美眉，MM=我的宝贝儿), 信区: JobHunting
: 标 题: 问道 面试题
: 发信站: BBS 未名空间站 (Wed Aug 18 20:54:55 2010, 美东)
: Line segment between 0 and 1. Choose two points randomly on the line. What
: is the average distance between them?
: 没有思路，谁给点提示或者参考，多谢。
| w******g
发帖数: 67 | | w******g
发帖数: 67 | 6 在网上看到的题目，还没面试呢：(
【在 l******f 的大作中提到】
: double integral
: btw, which type of business you interviewed? IT? stat?
| s****n
发帖数: 1237 | 7 I know Jacobian should be right, but I couldn't get it. (haven't used this
for years :)
We know with u[0,1] for U and V, X=U-V is a triangle with centers (-1,0),(0,
1),(1,0).
However using Jocobian transformation,
U=X+Y, V=Y and |J(x,y)|=1
f(u)*f(v)=1*1.
g(x,y)=1*1 = 1, with Y=V in [0,1], we will get g(x)=1, which is not right.
What did I miss? 3ks
transformation
【在 f***a 的大作中提到】
: More generic solution:
: U~f(u),V~f(v), and X=U-V.
: You want to find distribution of X.
: Simply let Y=V.
: since U,V are indedendent => f(u,v)=f(u)f(v)
: => g(x,y)=f(u(x,y),v(x,y))*|J(x,y)|, where J(x,y) is Jacobian transformation
: matrix.
: => g(x)= /int g(x,y) dy
: from here, you should have no problem to find the answer.
| f***a
发帖数: 329 | 8 You need include U,V regions in the density function.
f(u,v)=I(0
this
1,0),(0,
right.
【在 s****n 的大作中提到】
: I know Jacobian should be right, but I couldn't get it. (haven't used this
: for years :)
: We know with u[0,1] for U and V, X=U-V is a triangle with centers (-1,0),(0,
: 1),(1,0).
: However using Jocobian transformation,
: U=X+Y, V=Y and |J(x,y)|=1
: f(u)*f(v)=1*1.
: g(x,y)=1*1 = 1, with Y=V in [0,1], we will get g(x)=1, which is not right.
: What did I miss? 3ks
:
| c******r
发帖数: 300 | 9 Use order statistics and the fact that uniform order stat follows beta
distribution, i.e.,
U(2) ~ Beta(2,1), U(1) ~ Beta(1,2)
E(U(2) - U(1)) = E(U(2)) - E(U(1)) = 2/3 - 1/3 = 1/3
【在 w******g 的大作中提到】
: 在网上看到的题目，还没面试呢：(
| s********7
发帖数: 52 | 10 double integral abs(y-x) for x,y~U[0,1].
result is 1/3 | | | D**u
发帖数: 204 | 11 Connect 0 and 1 to make the line segment a circle. Let the connection be
point A, and the 2 random points be B and C.
By symmetry, the average distance between B and C is 1/3.
【在 w******g 的大作中提到】
: 在网上看到的题目，还没面试呢：(
| w*********l
发帖数: 1337 | 12 这个很直观啊。楼上什么夹克比看的我云里雾里的。就是一个E(|X2 - X1|)
【在 s********7 的大作中提到】
: double integral abs(y-x) for x,y~U[0,1].
: result is 1/3
| c*****w
发帖数: 50 | 13 L=|x1-x2|
Pr(L=x) ~ C*(1-x) where x is in [0,1) ==> C = 2 by normalization
==> E(L) = 1/3
【在 w******g 的大作中提到】
: 在网上看到的题目，还没面试呢：(
| s****i
发帖数: 216 | 14 答案是1/3 ?
想象一个二维坐标系， 在0-1的正方形内， 每个点(x,y)分别代表两个points在直线的
长度, \int
|x-y| dxdy =1/3
What
【在 w******g 的大作中提到】
: 在网上看到的题目，还没面试呢：(
| p*****k
发帖数: 318 | | M*****y
发帖数: 666 | 16 strong agree! zan
【在 D**u 的大作中提到】
: Connect 0 and 1 to make the line segment a circle. Let the connection be
: point A, and the 2 random points be B and C.
: By symmetry, the average distance between B and C is 1/3.
|
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