Let $X_n = X_1, X_2,..., X_n$ be a random sample of $X \sim U(0, \theta)$, where $\theta$ is an unknown parameter. Assuming confidence level $1 — \alpha$, find confidence interval for $\theta$ where:
a) n = 2
b) n $\geqslant$ 100
I've got answers for this question yet I still cannot solve it. I need an explanation.
Answers:
a) $\langle\frac{2\overline{X}_2}{2-\sqrt{\alpha}},\frac{2\overline{X}_2}{\sqrt{\alpha}}\rangle$
b) $\langle\frac{2\overline{X}_{100}}{2-\sqrt{\alpha}},\frac{2\overline{X}_{100}}{\sqrt{\alpha}}\rangle$