³  The formula for the truncated mean given in Johnson and Kotz (1971, p. 70) is only valid for a zero-mean vector or after demeaning all variables appropriately. For non-zero means \(\bfmu =(\bfmu _1, \bfmu _2)'\) it will be \((\boldsymbol {\xi '_1}, \bfmu _2 + (\boldsymbol {\xi '_1} - \bfmu _1) \bfV ^{-1}_{11} \bfV _{12})\).