I am really confused on how to find a pivot, it seems that it's just always derived randomly and on top of that even though it's defined that a pivot should nto depend on θ the pivot function always has θ in it? Doesn't that mean it depends on θ? Like, for this example below: Example Pivot Problem
It says in the solution that U = Y/θ doesn't depend on θ so it can be used as a pivot. What?? How did we arrive at U = Y/θ in the first place, was it just be guessing? And if U has θ in its function then doesn't that precisely mean that it does depend on θ? I'm very confused