'Consider once again the case of univariate missing data MAR for two bivariately normal variables, where the first variable, X1; is completely observed, and m observations

(for convenience, the first m) on the second variable, X2, are missing.

(a) Let A'

2j1 and B'

2j1 represent the intercept and slope for the complete-case least-squares regression of X2 on X1. Show that A'

2j1 and B'

2j1 are the ML estimators of α2j1 and β2j1.

(Hint: Use Equations 20.6 giving the ML estimators of µ1, µ2, σ2 1, σ2 2, and σ12.)

(b) Show that the M step from the first iteration of the EM algorithm (see Equations 20.8 and 20.9 on page 618 for the E step) produces the ML estimates (given in Equations 20.6 on page 616). That is, demonstrate that the EM algorithm converges in a single iteration.