Does linearly dependent imply statistically dependent?

From: wangxu78@xxxxxxxxx
Date: 4 May 2005 10:10:10 -0700

Given three random vectors X, Y, and Z.
We say X, Y, Z are linearly dependent if X = aY + bZ, where a and b are
scalar numbers and at least one of them is not zero.
Does this imply that X, Y and Z are also statistically dependent?

Thanks a lot
Sophia

.

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