Let $\displaystyle X_1, ... X_n$ be a random sample from the density function given by,

$\displaystyle f(x;\theta) = (\frac{1}{\theta})rx^{r-1}e^{-x^{r}/\theta}$

0 otherwise, $\displaystyle \theta > 0, x > 0$ for known r.

Find a sufficient statistic and maximum likelihood for $\displaystyle \theta$. Argue that the maximum likelihood estimator is also sufficient for $\displaystyle \theta$