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Let U, V and W be i.i.d. random variables with uniform distribution on [0,1]. Find the distribution of (U*V)^W.

I tried conditioning on the values of V and W to get a double integral over the unit square but I ended up having to integrate 1/v from 0 to 1 which is clearly wrong.

Rory
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  • I think I know where your trouble is coming in getting the $1/v$, and there is a simple fix, but can you show your work so I can see exactly what you are doing? – Michael Jun 01 '17 at 20:24
  • looks uniform to me – Henry Jun 01 '17 at 20:47
  • This was asked before on the site. 2. Indeed the result is uniform on (0,1). 3. Standard methods work here. 4. You do not show what you did so how can we help?
    • – Did Jun 01 '17 at 20:54
  • @Did: Slightly in OP's defense, it sounds like OP is trying to evaluate:

    $$P((UV)^W\leq x)=\int_0^1\int_0^1\int_0^{x^{1/w}/v}dudvdw,$$

    which is a somewhat different approach from the answers in the duplicate question.

     – Alex R. Jun 01 '17 at 21:13
  • Yes that's exactly what I tried doing – Rory Jun 02 '17 at 08:03