About the EM algorithm example in deGroot/Schervish I am confused about one part in the EM example for a bivariate normal distribution in the book by deGroot & Schervish (Example 7.6.15).
The part I do not understand is where the authors claim that the "conditional mean of $(X_{4,2} - \mu_2)^2$ would then be $212.8 + (193.3 - \mu_2)^2$."
I suppose by the "conditional mean of $(X_{4,2} - \mu_2)^2$, they mean the conditional variance of $X_{4,2}$. But then I am unable to figure out why that should be the sum of those two terms. 212.8 is the variance of the conditional distribution of $X_{4,2}$
 A: I am re-posting the question with more details. The example in question is from the book "Probability and Statistics" by deGroot & Schervish, Example 7.6.15.
It is required to estimate the means and variances of Heights and Weights, given the data below with missing values. The two variables are assumed to form a bivariate normal distribution. The data are:
Height: 72, 70, 73, 68, 65, $X_{6,1}$ 
Weight: 197, 204, 208, $X_{4,2}$, $X_{5,2}$, 170
The method followed is the EM algorithm, with the initial means and sd's taken to be those of the non-missing data.
The authors take as initial guesses:
    the two means calculated from the non-missing data for each variable: 69.60 and 194.75 
    the two sd's - but they are incorrect as printed in the book: 2.87 and 14.82 
    and the correlation coefficient for the three complete cases: 0.1764
So the initial parameter guesses for the EM algorithm for the bivariate normal distribution are: 
$\theta^0$ = (69.60, 194.75, 2.87, 14.82, 0.1764)
The conditional distribution for $X_{4,2}$ given the data and $\theta^0$ is a normal distribution with mean 193.3 and variance 212.8 (correct - I have verified this).
Then, the next line says: 
The conditional mean of $(X_{4,2} − \mu_2)^2$ would then be $212.8 + (193.3 − \mu_2)^2$.
That is what I am unable to figure out. Presumably, by the "conditional mean of $(X_{4,2} − \mu_2)^2$", the authors mean the conditional variance of $X_{4,2}$? But I still cannot see where the above expression ($212.8 + (193.3 − \mu_2)^2$) comes from.
Any help is welcome...
