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Problem #1: Using a bar of length µ, you are going to lay out a square plot in which the length of each side will be length µ. Thus the area of the plot will be u. However, you do not know the value of u and so you decide to make 19 independent measurements of the bar, Xi = 1,...,n}. Assume that each X has meanu (unbiased measurement) and variance o² = 0.5. (a) Find the bias of the random variable X² as an estimator for ². (b) For what value of k is the estimator X2 - ks² unbiased for u²?

Problem #1: Using a bar of length µ, you are going to lay out a square plot in which the length of each side will be length µ. Thus the area of the plot will be u. However, you do not know the value of u and so you decide to make 19 independent measurements of the bar, Xi = 1,...,n}. Assume that each X has meanu (unbiased measurement) and variance o² = 0.5. (a) Find the bias of the random variable X² as an estimator for ². (b) For what value of k is the estimator X2 - ks² unbiased for u²?

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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Problem #1: Using a bar of length, you are going to lay out a square plot in which the length of each side will be length u. Thus the area of the plot will be u. However, you do not know the value of u and so you decide to make 19 independent measurements of the bar, (Xi = 1,...,n}. Assume that each X has mean (unbiased measurement) and variance o² = 0.5. Problem #1(a): Problem #1(b): (a) Find the bias of the random variable ² as an estimator for ². (b) For what value of k is the estimator X2 - ks2 unbiased for u²? answer correct to 4 decimals answer correct to 4 decimals
Transcribed Image Text:Problem #1: Using a bar of length, you are going to lay out a square plot in which the length of each side will be length u. Thus the area of the plot will be u. However, you do not know the value of u and so you decide to make 19 independent measurements of the bar, (Xi = 1,...,n}. Assume that each X has mean (unbiased measurement) and variance o² = 0.5. Problem #1(a): Problem #1(b): (a) Find the bias of the random variable ² as an estimator for ². (b) For what value of k is the estimator X2 - ks2 unbiased for u²? answer correct to 4 decimals answer correct to 4 decimals
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