EB1B, 这样的offer letter 行吗？ - 未名空间MITBBS历史存档

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EB1B, 这样的offer letter 行吗？

EB1B, 这样的offer letter 行吗？# Immigration - 落地生根

a*r2010-04-15 07:04

1 楼

Given two i.i.d uniform random points x and y on the interval [0,1] , what
is the average size of the smallest of the three resulting intervals?

m*s2010-04-15 07:04

2 楼

research associate
the position will be a 12-month 100% appointment at a monthly salary of xxx
....
..
this offer is not intended to create a contract of employment for any
specific period of time and in contingent upon your eligibility to work in the US. Also it is contingent upon the approval of the Provost.In your case, we have every reason to believe such actions will be forthcoming.....

j*42010-04-15 07:04

3 楼

1/9

【在 a***r 的大作中提到】

: Given two i.i.d uniform random points x and y on the interval [0,1] , what
: is the average size of the smallest of the three resulting intervals?

l*52010-04-15 07:04

4 楼

怎么看都象是在推卸责任, 根本不是一份JOB OFFER

l*a2010-04-15 07:04

5 楼

verified by simulation.

【在 j*****4 的大作中提到】

: 1/9

m*s2010-04-15 07:04

6 楼

it 就这么写的，我也觉得怪怪的

I*A2010-04-15 07:04

7 楼

怎么算的？

【在 j*****4 的大作中提到】

: 1/9

g*e2010-04-15 07:04

8 楼

If you are already a faculty, try Eb1A first.
Eb1b can be your backup

j*42010-04-15 07:04

9 楼

Let x,y,z be the length of each interval.
So we have x+y+z=1 (0(see attachment).If we just want to know the average of each interval,that
is the centroid of x(or y,z)(1/3, according to middle school knowledge).
The average(expectation) of the smallest interval will be x-coordinate of
the centroid of shadowed small triangle.(xThat is 1/3*1/3.

【在 I**A 的大作中提到】

: 怎么算的？

I*A2010-04-15 07:04

10 楼

thanks, though i still didn't get it..

【在 j*****4 的大作中提到】

: Let x,y,z be the length of each interval.
: So we have x+y+z=1 (0: (see attachment).If we just want to know the average of each interval,that
: is the centroid of x(or y,z)(1/3, according to middle school knowledge).
: The average(expectation) of the smallest interval will be x-coordinate of
: the centroid of shadowed small triangle.(x: That is 1/3*1/3.

c*e2010-04-15 07:04

11 楼

Your answer is correct. It is 1/9. I verified by integration.
A solution with 2-D integration is easier for people to understand.
It is about [0,1]*[0,1]. Look at the upper left triangle xy
part can be done by symmetricty.)
It can be divided by 3 triangular parts, centered at (1/3,2/3).
In each part, the expectation of the smallest of the 3 interval
lengths min{x, y-x, 1-y} is 1/9. So is the average on the upper left
triangle x

【在 j*****4 的大作中提到】

v*w2010-04-15 07:04

12 楼

awesome
joson's sol is coll too, but the shaded area is not correct

【在 c**********e 的大作中提到】

: Your answer is correct. It is 1/9. I verified by integration.
: A solution with 2-D integration is easier for people to understand.
: It is about [0,1]*[0,1]. Look at the upper left triangle xy
: part can be done by symmetricty.)
: It can be divided by 3 triangular parts, centered at (1/3,2/3).
: In each part, the expectation of the smallest of the 3 interval
: lengths min{x, y-x, 1-y} is 1/9. So is the average on the upper left
: triangle x: