1. Consider a Gaussian statistical model X₁, ..., Xn ~ N(0, 0), with unknown > 0. Note thatVar (X) = 0 and Var (X²) = 20². To simplify the notation, define X = E=₁ X²/n.Prove that = X is the maximum likelihood estimator for 0, and verify that it(a)is unbiased.(b)Prove that the expected Fisher information for is equal to n/(20²), and checkif the maximum likelihood estimator for attains the Cramer-Rao lower bound.(c)Prove that the maximum likelihood estimator for is based on a minimalsufficient statistic.(d)Identify the parameters of a Gaussian density which is approximately propor-tional to the likelihood function of 0, in a neighbourhood of its maximum likelihoodestimator.

In this step, we find the Maximum Likelihood Estimator of θ and prove that this estimator is…

Answered: 1. Consider a Gaussian statistical…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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