  As alternatives to the normal distributions, $t$ distributions are widely
applied in robust analysis for data with outliers or heavy tails. The
properties of the multivariate $t$ distribution are well documented in Kotz and
Nadarajah's book, which, however, states a wrong conclusion about the
conditional distribution of the multivariate $t$ distribution. Previous
literature has recognized that the conditional distribution of the multivariate
$t$ distribution also follows the multivariate $t$ distribution. We provide an
intuitive proof without directly manipulating the complicated density function
of the multivariate $t$ distribution.
