Exact expectations and variances have been obtained for the maximum likelihood estimates of the elements of the mean vector and covariance matrix of the multivariate normal distribution when a subset of the variates does not have observations on some sampling units. The biases, variances, and mean square errors of the estimates are compared with those of the usual estimates computed from the complete observation vectors. When the correlations between the complete and incomplete sets of variates are small the multivariate missing value estimates are less efficient in the mean square error sense.