Let x1 xn be iid random variables having the lebesgue pdf

Question

Let X₁, ..., X_n be i.i.d. random variables having the Lebesgue p.d.f. θ^-1e^-(x-θ)/θI_(θ,∞)(x), where θ > 0 is an unknown parameter.

(a) Find a statistic that is minimal sufficient for θ.

(b) Show whether the minimal sufficient statistic in (a) is complete.