  In the present article we derive an explicit expression for the trun- cated
mean and variance for the multivariate normal distribution with ar- bitrary
rectangular double truncation. We use the moment generating ap- proach of
Tallis (1961) and extend it to general {\mu}, {\Sigma} and all combinations of
truncation. As part of the solution we also give a formula for the bivari- ate
marginal density of truncated multinormal variates. We also prove an invariance
property of some elements of the inverse covariance after trunca- tion.
Computer algorithms for computing the truncated mean, variance and the
bivariate marginal probabilities for doubly truncated multivariate normal
variates have been written in R and are presented along with three examples.
