4.5 Suppose data are an incomplete random sample on Y1 and Y2, where Y1 given θ = (????1, ????11, ????20⋅13, ????21⋅13, ????23⋅13, ????22⋅13) is N(????1, ????11) and Y2 given Y1 and θ is N(????20⋅13 + ????21⋅13Y1 + ????23.13Y2 1 , ????22⋅13). The data are MCAR, the first r units are complete, the next r1 units observe Y1 only, and the last r2 units observe Y2 only. Consider the properties of Buck’s method, applied to

(a) Y1 and Y2, and

(b) Y1, Y2, and Y3 = Y2 1 (so that Y3 has the same pattern as Y1 and is imputed from the regression of Y3 on Y1, Y2), for deriving estimates of (i) the unconditional means E(Y1 ∣ θ) and E(Y2 ∣ θ), and (ii) the conditional means E(Y1 ∣ Y2, θ), E(Y2 1 ∣ Y2, ????), and E(Y2 ∣ Y1, θ).