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

**crazymonkey** · April 10th 2009, 10:19 AM

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.

**NonCommAlg** · April 10th 2009, 10:59 AM

Originally Posted by crazymonkey

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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