I am having some problems with the second point of this exercise
Let $(X_1, \dots, X_n)$ be a random sample extracted from a population $X$ that is distributed as a uniform $(0, \theta)$ and let $Y_n = \max (X_1, \dots, X_n)$.
1) If one puts $Q( \theta, X_1 \dots X_n) = Y_n / \theta$ prove that the distribution of $Q$ does not depend on $\theta$.
2) Show how it is then possible to construct a confidence interval for $\theta$.
For point 1 I proceeded as follows (aside from the obvious cases $y < 0, y > 1$) $$P(Y_n / \theta < y) = P(Y_n < y\theta) = (F_X(y \theta))^n = (y\theta / \theta )^n = y^n$$
For point 2 I am a bit lost, anyone mind lending a hand?