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  1. Let $X, Y$ be random variables. If $\rho(X,Y) = a$ (Correlation), where $a \in (0,1)$, what can be said about the relationship between $X$ and $Y$? Is it true that $Y = bX + c + Z$, where $Z$ is a random variable? If it is true then how is $|Z|$ related to the correlation a?

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