Let x1 xn be iid observations obtain a umvue of a in the

Question

Let X₁, ..., X_n be i.i.d. observations. Obtain a UMVUE of a in the following cases.

(a) X_i has the exponential distribution E(a, θ) with a known θ and an unknown a ≤ 0.

(b) X_i has the Pareto distribution Pa(a, θ) with a known θ > 1 and an unknown a ∈ (0, 1].