a. Let X be a single observation from a normal distribution with mean and withvariance 02, where > 0. Find the maximum likelihood estimator of 0².b. Let X₁, X2, . . . , Xn be independent identically distributed random variablesfrom a N(μ, o2) distribution where the variance o² is known. We want to testHo : μ = μo against H, : μ + μο(i) Derive the likelihood ratio test.(ii) Let A be the likelihood ratio. Show that -2log A is a function of (X - μo).Assuming that Ho is true, find P(-2 log > 3.84).

The normal distribution is the most commonly used continuous distribution. The random variable which…

Answered: a. Let X be a single observation from a…

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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a. Let X be a single observation from a normal distribution with mean and with variance 02, where > 0. Find the maximum likelihood estimator of 0².