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The relationship between the Covariance & Energy of a random signal

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emicho

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Let's say I have the below random signal:
Y[n] = [y(n) y(n-1) y(n-2) .... y(1)]

I have two random variables now:
The first one χ which express the maximum eigenvalue of the covariance matrix of Y.
The second one λ which express the energy of the random signal.

Now my question is:
Are the two random variables independent or dependent ,when whether signal samples :
y(n),y(n-1) .... are IID or correlated with each other.

By intuition the two random variables should be correlated !?
isn't it right!?
 

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