scale-mixture in exercise we viewed the multivariate student ta distribution as scale-mixture of the ( id distribution in this exercisewe consider similar transformationbut now / ( sis not divided but is multiplied by with gamma( / / ) / ( where and are independent and bessel distribution (ashowusing exercise that for / id and the random vector has -dimensional bessel distributionwith densityka ( : -( + )/ ( + )/ kxk( - )/ kxk ( - )/ pd/ ( / rd where is the modified bessel function of the second kind given in ( we write bessela ( id random vector is said to have bessela (usdistribution if it can be written in the form ( by the transformation rule ( )its density is given by |ska ( - / ( )special instances of the bessel pdf includeexp( | | ( |xk (xexp(- | | ( exp - (( )/ ) / kd+ (xexp kxk rd ( ) / (( )/ note that is the (scaledpdf of the double-exponential or laplace distribution (bgiven the data { xn in rd we wish to fit bessel pdf to the data by employing the em algorithmaugmenting the data with the vector [ ]of missing data we assume that is known and show that conditional on (and given th)the missing data vector has independent componentswith gig(abi ( )/ )with bi :ks- / (xi ) (cat iteration of the em algorithmlet ( (sg( tth( - be the density of the missing datagiven the observed data and the current parameter guess th( - show that the expected complete-data log-likelihood is given byn (th:eg(tln (ts thbi (thw( - constanti = (twhere bi (thks- / (xi ) and  ( - (th ( - + )/ - ( - :   ( - ( - bi (th( - bi (th ( - )/ bi (th ( (dfrom ( derive the -step of the em algorithm that isshow how th(tis updated from th( -