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 æ = (1, T2, … .. , In) 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(r.) = 61 + 62, E(4.) = 61 – 62, Var(r,) = Var(y,) = o² (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 0z 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 estimates for 61, 02 and o based on your estimators in (a).

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 æ = (1, T2, … .. , In) 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(r.) = 61 + 62, E(4.) = 61 – 62, Var(r,) = Var(y,) = o² (a) Assuming X and Y are normally distributed, determine the maximum likelihood estimators of 01, 0z 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 estimates for 61, 02 and o based on your estimators in (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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