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a. Suppose Y; = B1x; + €;, i = 1, ..., n. In this equation x is non-random, B1 is a parameter (unknown but not random), e ~ not adjust it to be unbiased. N(0, 0), and €1,..., En are independent. Find the MLE of o². Is it unbiased? If

a. Suppose Y; = B1x; + €;, i = 1, ..., n. In this equation x is non-random, B1 is a parameter (unknown but not random), e ~ not adjust it to be unbiased. N(0, 0), and €1,..., En are independent. Find the MLE of o². Is it unbiased? If

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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a. Suppose Y; = B1x; + €;, i = 1,...,n. In this equation x is non-random, ß1 is a parameter (unknown but not random), e ~ not adjust it to be unbiased. N (0, o), and €1, ..., En are independent. Find the MLE of o². Is it unbiased? If b. Refer to question (a). Let S2 be the unbiased estimator of o?. Use all the details (distribution theory, (n-1)S? independence, moment generating functions) to find the distribution of c. Use the result from question (b) and also the distribution of 6Bị to construct a t ratio. What are the degrees of freedom of this t ratio? Note: Bị is the MLE of B1. - a prediction interval for Y can be constructed for a given new value x0. Note: The d. Explain how a 1 prediction of Y is given by Yo = B1x0. Also, assume that Yo is not one of the Y1,..., Yn values.
Transcribed Image Text:a. Suppose Y; = B1x; + €;, i = 1,...,n. In this equation x is non-random, ß1 is a parameter (unknown but not random), e ~ not adjust it to be unbiased. N (0, o), and €1, ..., En are independent. Find the MLE of o². Is it unbiased? If b. Refer to question (a). Let S2 be the unbiased estimator of o?. Use all the details (distribution theory, (n-1)S? independence, moment generating functions) to find the distribution of c. Use the result from question (b) and also the distribution of 6Bị to construct a t ratio. What are the degrees of freedom of this t ratio? Note: Bị is the MLE of B1. - a prediction interval for Y can be constructed for a given new value x0. Note: The d. Explain how a 1 prediction of Y is given by Yo = B1x0. Also, assume that Yo is not one of the Y1,..., Yn values.
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