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Math Help - Is the function 1/|x+y| a joint probability density function?

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    Is the function 1/|x+y| a joint probability density function?

    Is the function \frac{1}{|x+y|} a joint probability density function? That is, is \int\hspace{-6pt}\int_{\mathbb{R}^2} \frac{1}{|x+y|} \ dA equal to 1 and is \frac{1}{|x+y|} nonnegative?

    This problem is really giving me a headache, been attempting it for a week now and the deadline's today.
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    Quote Originally Posted by crazymonkey View Post

    Is the function \frac{1}{|x+y|} a joint probability density function? That is, is \int\hspace{-6pt}\int_{\mathbb{R}^2} \frac{1}{|x+y|} \ dA equal to 1 and is \frac{1}{|x+y|} nonnegative?

    This problem is really giving me a headache, been attempting it for a week now and the deadline's today.
    no! the integral is divergent: your function is positive wherever is defined. show that the integral is \infty in the first quadrant and thus it's divergent over \mathbb{R}^2.
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