q******1
发帖数: 220 | 1 If the correlation coefficient of X, Y is 0.7 and the correlation
coefficient of Y, Z, then what are the smallest and largest possible value
of the correlation coefficient of X and Z.
多谢解答。 | q******1
发帖数: 220 | 2 不好意思,漏打了个条件,the correlation coefficient of Y, Z is 0.8.
刚刚又考虑的一下，想出来了。。。
从correlation coefficient的公式说起r(X,Y)=cov(X,Y)/sqrt(Var(X),Var(Y)),
where cov(X,Y)=E(XY)-EXEY and X, Y are r.v. on (S, P). So r(X,Y)=cosA, A is
the angle between the vector X-EX and Y-EY in L^2(P).
Therefore, original question becomes a simple question in linear algebra. |
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