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Thread: 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 $\displaystyle \frac{1}{|x+y|}$ a joint probability density function? That is, is $\displaystyle \int\hspace{-6pt}\int_{\mathbb{R}^2} \frac{1}{|x+y|} \ dA$ equal to 1 and is $\displaystyle \frac{1}{|x+y|}$ 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 $\displaystyle \frac{1}{|x+y|}$ a joint probability density function? That is, is $\displaystyle \int\hspace{-6pt}\int_{\mathbb{R}^2} \frac{1}{|x+y|} \ dA$ equal to 1 and is $\displaystyle \frac{1}{|x+y|}$ 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 $\displaystyle \infty$ in the first quadrant and thus it's divergent over $\displaystyle \mathbb{R}^2.$
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