The exponent is then: 
(X-#-e) Lx (&-u-e) = 
= a T -— ] A. d ^. T xL sufficre 
(2-1) T ex (xu) (2-1) E x e estimatc 
l 
ft! . T 
- * TOTO 4T 
€ A x (X-u) +¢ LE say T T 
Here we can write: 
X-u * A(j - n) 
and 
Tol , 
€ = ZU T C t 
using U.A-o we find that T =o and T =o 
2 
Further development gives: 
Sat But Le al 21 wn 
= Gn) A A (zn) = (5-7) ge ($-m) 
and with (1.47) 
Tog 
tt 
With these results the j-p.d.f. of x is: 
f(x, X) =Clexp | 2 (y-n) Les (9-n) -i (t Et 5 | 
'lt is possible to decompose C in two factors C; and C, 
so that: 
Il 
^ T--1 A T.-1 
fox T C, exp 16-0 LS 5-n | C, exp E t's | 
14 731 tete 
The j.p.d.f. of x can be written as the product of the j.p.d.f. 
of the estimator $ and the j-p:d.f. of the variates t, the mis- 
closures of the condition equations.