sufficiency
Let X1,...,Xn be iid with density $\displaystyle f(x;\theta )=\frac{2}{3\theta}(1\frac{x}{3\theta})$ for $\displaystyle 0<x<3\theta$ and let $\displaystyle \widehat{\theta}=\widehat{X}$ be an estimate of $\displaystyle \theta$.
I determined that the estimator is unbiased and consistent. But now I have to determine wheter it is sufficient. I tried to factor the jpd function, but I got $\displaystyle (1\frac{x}{3\theta})^{n}$ and I don't know how to handle... Trying a counter example I only did in discrete cases before, so I don't know how to do that as wel. Can someone give me a hint for a approach?
Thanks!
