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...

Extracted 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 x = set for positive bias, and the other n measurements (y1, Y2, . .. , Yn), taken with a setting of negative bias, so that (x1, x2, ..., xn) are taken with the instrument E(x;) = 01 + 02, E(y;) = 01 – 62, Var(x;) = Var(y;) : g² (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 estimates for 01, 02 and o based on your estimators in (a).