= EM for an independent missing normal coordinate
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For independent normal coordinates, an unobserved first coordinate has conditional law equal to its current marginal <normal distribution>, even when the second coordinate of that observation is known. Thus its E-step first moment is $\mu_1^{(t)}$ and second moment is $(\mu_1^{(t)})^2+v_1^{(t)}$. With three observed first coordinates and one missing value, the mean update is $(\sum_{i=1}^3x_{i1}+\mu_1^{(t)})/4$ and the <variance> update is $[\sum_{i=1}^3(x_{i1}-\mu_1^{(t+1)})^2+v_1^{(t)}+(\mu_1^{(t)}-\mu_1^{(t+1)})^2]/4$. The <conditional variance> term is essential: filling in only the conditional mean is not the <expectation-maximization algorithm>.
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