Let X₁,..., Xₙ be n i.i.d. random variables with distribution N (θ,θ) for some unknown θ>θ.
In the last homework, you have computed the maximum likelihood estimator for θ in terms of the sample averages of the linear and quadratic means, i.e. Xₙ and X²ₙ, and applied the CLT and delta method to find its asymptotic variance.
In this problem, you will compute the asymptotic variance of θ via the Fisher Information
Finally, what does this tell us about the asymptotic variance of θ?
V (θ) = ___