Solution
= Solution
Factorisation of the likelihood $(1-\theta)^{-n}1_{\{\theta\le X_{(1)}\}}$ shows that $T=X_{(1)}$ is sufficient: conditional on it, the sample law is independent of $\theta$.
= Solution
Factorisation of the likelihood $(1-\theta)^{-n}1_{\{\theta\le X_{(1)}\}}$ shows that $T=X_{(1)}$ is sufficient: conditional on it, the sample law is independent of $\theta$.