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12. To determine the weights of w1, wz and wz of three objects A1, Az and A3, the following weighing design was adopted. The objects were first weighed separately (Aj then Az then A3) and then all three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing are denoted by r1, 12, Iz and 14 respectively with the expected values and variances given by E(r1) = wi, E(x2) = wz, E(13) = ws E(1.) = wi+w2 +ws and Var(x,) = of, i = 1,2, 3. (a) By an appropriate method of estimating w, w2, and w3, generate their normal equations and present in a matrix form. (b) Hence or otherwise, find the least square estimators of wi, wz, and wz if Var(r,) = o², 1, 2, 3. (c) Given that z, = 2.2, x2 = 1.7, 13 = 6.0, 14 = 9.5 and o = 1.5, find an estimate for w.

12. To determine the weights of w1, wz and wz of three objects A1, Az and A3, the following weighing design was adopted. The objects were first weighed separately (Aj then Az then A3) and then all three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing are denoted by r1, 12, Iz and 14 respectively with the expected values and variances given by E(r1) = wi, E(x2) = wz, E(13) = ws E(1.) = wi+w2 +ws and Var(x,) = of, i = 1,2, 3. (a) By an appropriate method of estimating w, w2, and w3, generate their normal equations and present in a matrix form. (b) Hence or otherwise, find the least square estimators of wi, wz, and wz if Var(r,) = o², 1, 2, 3. (c) Given that z, = 2.2, x2 = 1.7, 13 = 6.0, 14 = 9.5 and o = 1.5, find an estimate for w.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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12. To determine the weights of w1, w2 and wz of three objects Aj, A2 and A3, the following weighing design was adopted. The objects were first weighed separately (A1 then A2 then A3) and then all three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing are denoted by r1, 12, 1z and r4 respectively with the expected values and variances given by E(x1) = w1, E(r2) = w2, E(r3) = w3 E(x4) = w1+ w2 + w3 and Var(r,) = of, i= 1, 2, 3. (a) By an appropriate method of estimating w1, wz, and w3, generate their normal equations and present in a matrix form. (b) Hence or otherwise, find the least square estimators of w1, w2, and wz if Var(x;) = o², 1, 2, 3. i = (c) Given that , = 2.2, x2 = 1.7, xz = 6.0, x4 = 9.5 and o = 1.5, find an estimate for w1. %3D
Transcribed Image Text:12. To determine the weights of w1, w2 and wz of three objects Aj, A2 and A3, the following weighing design was adopted. The objects were first weighed separately (A1 then A2 then A3) and then all three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing are denoted by r1, 12, 1z and r4 respectively with the expected values and variances given by E(x1) = w1, E(r2) = w2, E(r3) = w3 E(x4) = w1+ w2 + w3 and Var(r,) = of, i= 1, 2, 3. (a) By an appropriate method of estimating w1, wz, and w3, generate their normal equations and present in a matrix form. (b) Hence or otherwise, find the least square estimators of w1, w2, and wz if Var(x;) = o², 1, 2, 3. i = (c) Given that , = 2.2, x2 = 1.7, xz = 6.0, x4 = 9.5 and o = 1.5, find an estimate for w1. %3D
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