发信人: Icare (土豆自风流), 信区: Quant
标 题: Correlation of the larger and the smaller of two Uniform[0
发信站: BBS 未名空间站 (Sun Jun 25 10:53:18 2006)

Assume X1, X2 are both uniform[0,1] r.v.s

Xmax=max(x1, x2), Xmin=min(x1, x2).

Corr(Xmax, Xmin)=(E(XmaxXmin)-E(Xmax)E(Xmin))/Std(Xmax)Std(Xmin))

The key is to find out E(Xmax) and Var(Xmax). (Obviously, E(Xmin)=1-E(Xmax)
and Var(Xmax)=Var(Xmin).)

Easy to see E(Xmax)=2/3, and Var(Xmax)=1/18 because Xmax has a cdf of x^2 and
pdf of 2x.

Therefore, Corr=1/2.

-iCare-

问题：
1.两个uniform 分布，其中值大的和值小的correlation※ 修改:·BulletTooth 於 Jun 27 22:49:14 2006 修改本文·[FROM: 129.81.]
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 67.85.]