Hi! I'd be thankful if anyone could check my work to see if I've done this correct:

Let Y have a pdf:

Show that

is a pivotal quantity.

I start out with a new variable:

Mr F says: Small mistake here. The red 2 needs to be included.
So this is the distribution function of U. I take the derivative of that to find the pdf of U, which equals

Then

fulfils the conditions for a pivotal quantity. Which is:

1. a function of the sample measurement, Y and the unknown parameter

2. It's probability distribution does not depend on the parameter

.

Is this correct? Thanks in advance.