Here is a second one I'm not too sure what to do next :

Let and be independent, with respective probability density functions of the forms , , and , .

Find the distribution of .

Here's how it goes :

Let and .

The transformation is then specified by two functions :

and

And the inverse transformation is and giving

and

So the Jacobian of the transformation is given by

So

Hence using the theorem

In order to find we need to calculate over the range of .

This is where I get stuck. I'm assuming the range of is the same as the range of (so ).

But it doesn't seem to be integrable.

Plus I'm not sure what is meant by find the distribution of .

Does it mean identify the distribution of (i.e Normal, Gamma..) ?

Thanks for the help.