Let $X_1,...,X_n$, be iid random variables from the continuous uniform distribution on the interval $(a,b)$. Suppose that $a$ is known, find the UMVUE of parameter $b$.
I'm stuck with this question. I have been trying to find a complete and sufficient statistic for $b$, but I´m only able to find it for $U(0,b)$. Maybe this way is more complicated to find the UMVUE($b$) but I'm now interested in finding the complete and sufficient statistic for $b$. Any suggestions would be great!