If you have $n$ random variables that are iid with density $\frac{1}{p}e^{-x/p}$, how do you show that the sum of the $x_i$'s is a sufficient statistic?
Attempt: Take likelihood function and express in terms of $g(p)h(x)$ and use factorization theorem to show that it is a sufficient statistic. So likelihood = $\frac{1}{p^n} \exp(\sum \frac{-x_i}{p}) = \frac{1}{p^n} \exp(\frac{1}{p} \sum (-x_i))$.