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 $X_1$ which express the maximum eigenvalue of the covariance matrix of $Y$. The second one $X_2$ 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!?