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:
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.