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$X,Y$ and $Z$ are independent uniformly distributed on $[0,1]$

How is random variable $(XY)^Z$ distributed?

I had an idea to logarithm this and use convolution integral for the sum, but I'm not sure it's possible.

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    Why do you need to know? Also, does $(XY)^{\frac{1}{2}}$ mean $\sqrt{XY}$ or $-\sqrt{XY}$.2012-12-18

3 Answers 3