im working on the following problem:
$X_1$,....,$X_n$ are random variables, iid and uniformly distributed on the Interval $(0,\theta)$. Show that for all $\lambda_1$,$\lambda_2$ with $0<\lambda_1<\lambda_2<1$ and $\lambda_2^n - \lambda_1^n = 1-\alpha$ the interval $[\frac{M}{\lambda_2},\frac{M}{\lambda_1}]$ is a $1-\alpha$ confidence interval for $\theta$ ( with $M=max(X_1,...,X_n)$).
Ive only done this kind of problem for explicit values, applying the definition is a little bit too much for me at the moment. What ive done so far is to use the CLT to calculate the actual interval based on mean and variance. Since a uniform distribution is given here, that should not be too much of a problem. My main problem is to show that (given the interval) $P(I) \geq 1- \alpha $.
Thanks in advance