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Apart from the usual random errors of measurement, an instrument has one source of bias which cannot be totally eliminated by suitable adjustment. It is however possible to set the instrument so as to make the bias positive or negative. The instrument is used to take 2n independent measurements of a certain quantity; n of these measurements a = (x1, x2,..., ¤n) are taken with the instrument set for positive bias, and the other n measurements (y1, Y2, - .. , Yn), taken with a setting of negative bias, so that E(x:) = 01 + 02, E(¥4) = 01 – 62, Var(x;) = V ar(y;) = o? (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 02 and o. (b) A random the measurements from the two instruments are give in the table below Obtain Positive bias X: | 24.58 23.98 24.42 25.64 27.22 26.05 Negative bias Y: 23.32 23.04 22.45 23.78 27.00 22.48

Apart from the usual random errors of measurement, an instrument has one source of bias which cannot be totally eliminated by suitable adjustment. It is however possible to set the instrument so as to make the bias positive or negative. The instrument is used to take 2n independent measurements of a certain quantity; n of these measurements a = (x1, x2,..., ¤n) are taken with the instrument set for positive bias, and the other n measurements (y1, Y2, - .. , Yn), taken with a setting of negative bias, so that E(x:) = 01 + 02, E(¥4) = 01 – 62, Var(x;) = V ar(y;) = o? (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 02 and o. (b) A random the measurements from the two instruments are give in the table below Obtain Positive bias X: | 24.58 23.98 24.42 25.64 27.22 26.05 Negative bias Y: 23.32 23.04 22.45 23.78 27.00 22.48

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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20. Apart from the usual random errors of measurement, an instrument has one source of bias which cannot be totally eliminated by suitable adjustment. It is however possible to set the instrument so as to make the bias positive or negative. The instrument is used to take 2n independent measurements of a certain quantity; n of these measurements a = (x1, 82,- set for positive bias, and the other n measurements (y1, Y2, bias, so that ,In) are taken with the instrument Yn), taken with a setting of negative ... .... E(x;) = 01 + 02, E(y;)= 01 – 02, Var(x;) = Var(y;) = o? (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 02 and o. (b) A random the measurements from the two instruments are give in the table below Obtain Positive bias X: | 24.58 23.98 24.42 25.6 27.22 26.05 Negative bias Y: 23.32 23.04 22.45 23.78 27.00 22.48 estimates for 01, 02 and o based on your estimators in (a).
Transcribed Image Text:20. Apart from the usual random errors of measurement, an instrument has one source of bias which cannot be totally eliminated by suitable adjustment. It is however possible to set the instrument so as to make the bias positive or negative. The instrument is used to take 2n independent measurements of a certain quantity; n of these measurements a = (x1, 82,- set for positive bias, and the other n measurements (y1, Y2, bias, so that ,In) are taken with the instrument Yn), taken with a setting of negative ... .... E(x;) = 01 + 02, E(y;)= 01 – 02, Var(x;) = Var(y;) = o? (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 02 and o. (b) A random the measurements from the two instruments are give in the table below Obtain Positive bias X: | 24.58 23.98 24.42 25.6 27.22 26.05 Negative bias Y: 23.32 23.04 22.45 23.78 27.00 22.48 estimates for 01, 02 and o based on your estimators in (a).
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