A random sample of size $\displaystyle n$ is drawn from the pdf,

$\displaystyle f_Y(y;\theta) = e^{-(y-\theta)}$, $\displaystyle \theta\le y$

I can show that $\displaystyle Y_{max}$ is not sufficient by an example, but I am having a hard time showing that $\displaystyle Y_{min}$ is sufficient.