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Given the joint probability density function of $X$ and $Y$ is $$ f(x,y)=\cases{xy \exp\bigl(-\textstyle{1\over2}(x^2+y^2)\bigr),&$x>0,y>0$\cr 0\phantom{\Bigl[},& elsewhere.} $$ Find $P(X^2+Y^2>4)$.

What approach should I use to solve this question? Transformation?

Hope someone can help me !_!

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    Compute $\int_{\mathbb{R}^2}{f(x,y)I_{\{x^2+y^2<4\}}dx\,dy}$.2012-12-30
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    Yes, you should use a transformation to polar coordinates.2012-12-30

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