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1. Consider a Gaussian statistical model X₁,..., Xn~ N(0, 0), with unknown > 0. Note that Var (X) = 0 and Var (X²) = 20². To simplify the notation, define X = ₁ X²/n. (a) Love that mood eatimeter for 0, and verify that it (b) (c) is unbiased. Prove that the expect. m like that i 1100 ***tian for His eques #the Grame Pas lower bound. ator for is based on bęck (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 likelihood estimator.

1. Consider a Gaussian statistical model X₁,..., Xn~ N(0, 0), with unknown > 0. Note that Var (X) = 0 and Var (X²) = 20². To simplify the notation, define X = ₁ X²/n. (a) Love that mood eatimeter for 0, and verify that it (b) (c) is unbiased. Prove that the expect. m like that i 1100 ***tian for His eques #the Grame Pas lower bound. ator for is based on bęck (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 likelihood estimator.

MATLAB: An Introduction with Applications
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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1. Consider a Gaussian statistical model X₁,..., Xn~ N(0, 0), with unknown > 0. Note that Var (X) = 0 and Var (X2) = 20². To simplify the notation, define X = 1X²/n. (a) rove the stimeter for 0, and verify that it (b) (c) is unbiased. Prove that the expectext- erimum likemout on Breve **tion for # is equus Pas lower bound. food colimator for is based leck (d) 2 Identify the parameters of a Gaussian density which is approximately propor- tional to the likelihood function of 0, in a neighbourhood of its maximum likelihood estimator.
Transcribed Image Text:1. Consider a Gaussian statistical model X₁,..., Xn~ N(0, 0), with unknown > 0. Note that Var (X) = 0 and Var (X2) = 20². To simplify the notation, define X = 1X²/n. (a) rove the stimeter for 0, and verify that it (b) (c) is unbiased. Prove that the expectext- erimum likemout on Breve **tion for # is equus Pas lower bound. food colimator for is based leck (d) 2 Identify the parameters of a Gaussian density which is approximately propor- tional to the likelihood function of 0, in a neighbourhood of its maximum likelihood estimator.
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