Two objects with unknown weights ₁ and ₂ are weighed separately on a scale and together (both placed on the scale), giving three measurements x₁, x₂ and x₃. It is known from previous experience with the scale that measurements are independent and normally distributed about the true weights with variance 1.

It is known that the MLEs are ₁ = (2x₁ + x₃ x₂)/3 and ₂ = (2x₂ + x₃ x₁)/3.

(a) Obtain the information matrix I(₁, ₂)

(b) Does the estimator ₁ = (2X₁ + X₃ X₂)/3 attain the information lower bound for ₁? Give reasons for your answer.