作者fifs (^^)
站内Statistics
标题Re: 一个问题
时间Sat Jun 3 22:53:36 2006
※ 引述《Charles125 (4/27视小中友之夜)》之铭言：
: 我们知道
: Two independent random variables have zero correlation coefficient.
: 那为什麽
: Two random variables with zero correlation coefficient are independent
: 是错的
: 可以举一下反例吗
suppose that X,Y are random variables, and their joint p.d.f is following:
Y\X │-1 │ 0 │ 1
-----------------------
-1 │ 0 │ 1/4 │ 0
-----------------------
0 │1/4 │ 0 │1/4
------------------------
1 │ 0 │ 1/4 │ 0
we know that X,Y random variables have zero correlation coefficient
but, P(X=-1,Y=-1)=0 does not equal to P(X=-1)*P(Y=-1)=1/4 * 1/4 =1/16
thus, X and Y are not independent random variables.
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※ 编辑: fifs 来自: 59.104.101.24 (06/03 22:55)