※ 引述《Charles125 (4/27視小中友之夜)》之銘言：
: 我們知道
: Two independent random variables have zero correlation coefficient.
: 那為什麼
: Two random variables with zero correlation coefficient are independent
: 是錯的
: 可以舉一下反例嗎
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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※ 編輯: fifs 來自: 59.104.101.24 (06/03 22:55)