Hi. The question is:(adsbygoogle = window.adsbygoogle || []).push({});

Given X, Y and Z are all continuous, independant random variables uniformly distributed on (0,1), prove that (XY)^Z is also uniformly distributed on (0,1).

I worked out the pdf of XY=W. I think it's -ln(w). I have no idea at all how to show that W^Z is U(0,1).

What do I integrate, how do I know how to combine the pdfs, how do I know what the limits are, what substitutions should I make if I need to make one? Etc, really. I just don't know how to tackle this sort of problem at all. The pdf I have for W came from a picture, not any real understanding of what I was doing.

Thanks for any help :)

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# PDF of function of 3 continuous, uniform random variables?

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