# Independence of RV

Probability Level 2

A certain joint probability density function is given by the formula

$f_{XY} (xy) = \dfrac{\sqrt{\pi}}{2} x\sin (xy),$

where $x$ and $y$ are drawn from the rectangle $\big[0,\sqrt{\pi}\big]\times \big[0,\sqrt{\pi}\big].$

Are the random variables $X$ and $Y$ independent?

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