Question: The random vector ((X, Y)) has the joint density [f_{X, Y}(x, y)=8 x y, quad 0

The random vector \((X, Y)\) has the joint density

\[f_{X, Y}(x, y)=8 x y, \quad 0

Determine

(1) the correlation coefficient \(ho(X, Y)\),

(2) the regression line \(\tilde{y}=\alpha x+\beta\) of \(Y\) with regard to \(X\),

(3) the regression function \(y=m_{Y}(x)\).

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