-dimensional normal random vector (uscan be defined via an affine transformationx / zof standard normal random vector ( id )where / ( / ) in similar waywe can define -dimensional student random vector ta (usvia transformation / zs ( wherez ( id and gammaa are independenta and / ( / ) note that we obtain the multivariate normal distribution as limiting case for (ashow that the density of the ta ( id distribution is given by ! + (( )/ ta ( : kxk (pa) / ( / by the transformation rule ( )it follows that the density of ta (usis given by ta, ( )where ta, ( : / ta ( - / | [hintconditional on sx has ( id /sdistribution (bwe wish to fit tn (usdistribution to given data { xn in rd via the em method we use the representation ( and augment the data with the vector [ ]of hidden variables show that the complete-data likelihood is given by (ts thy ( / ) / ( + )/ - exp(si si ks- / (xi ) / ( / )( | / ( (cshow thatas consequenceconditional on the data and parameter ththe hidden data are mutually independentand ks- / (xi ) ( tthgamma (dat iteration of the em algorithmlet ( (sg( tth( - be the density of the missing datagiven the observed data and the current parameter guess th( - verify that the expected complete-data log-likelihood is given byan na nd (tln ln( pn ln ln |seg ln (ts th + - ks- / (xi ) eg(tln eg(ts = = show that ( - = ( - ( - ( ( - )- / (xi ( - ) ( - ( - eg(tln ps ln ln ( - eg(ts where ps :(ln ) is digamma function