I don't know how to express the problem to the form $f(x|\theta)=h(x)c(\theta)(\sum_{i=1}^{k}\omega_i(\theta)t_i(x))$
Let $X$ have pdf $f(x)=\frac{1}{\beta}e^{-(x-\alpha)/\beta}$, $x>\alpha$
Determine whether $f(x)$ is an exponential
a. if both $\alpha$ and $\beta$ are unknown.
b. if only $\beta$ is unknown
I thought those questions are same but it is not.