12. To determine the weights of w1, w2 and wz of three objects A1, 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, 82, Lz and a4 respectively with the expected values and variances given by E(r1) = w1, E(r2) = w2, E(x3) = w3 E(x4) = w1 + w2 +w'z and Var(x;) = io², i = 1,2, 3. (a) By an appropriate method of estimating w1, w2, 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;) = io², 1,2, 3. i = (c) Given that a1 = 2.2, x2 1.7, 13 6.0, a4 = 9.5 and o = 1.5, find the estimates for w and W3.

12. To determine the weights of w1, w2 and wz of three objects A1, 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, 82, Lz and a4 respectively with the expected values and variances given by E(r1) = w1, E(r2) = w2, E(x3) = w3 E(x4) = w1 + w2 +w'z and Var(x;) = io², i = 1,2, 3. (a) By an appropriate method of estimating w1, w2, 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;) = io², 1,2, 3. i = (c) Given that a1 = 2.2, x2 1.7, 13 6.0, a4 = 9.5 and o = 1.5, find the estimates for w and W3.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 7E: List the sample space of each experiment. Selecting a letter of the alphabet

See similar textbooks