Extracted text: 12. To determine the weights of wi, 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 1, 82, 83 and x4 respectively with the expected values and variances given by E(r1) = w1, E(r2) = w2, E(r3) = w3 E(x4) = wi + w2 + W3 and Var(x;) = io?, 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 V ar (x:) = io², 1, 2, 3. i = (c) Given that x1 2.2, r2 1.7, 2з — 6.0, 4 9.5 and σ= 1.5, find the estimates for w and W3.