Table 1. The possible arrangements of $U_1,U_2$ and $U_3$.

Different arrangements	Probabilities	(${\delta }_1,{\delta }_2$)	$X_1$ and $X_2$	Set
$U_3<U_1<U_2$	$\frac{{\lambda }_1{\lambda }_2}{({\lambda }_1+{\lambda }_3)({\lambda }_1+{\lambda }_2)}$	$(1,2)$	$X_1<X_2$	$I_{312}$
$U_1<U_3<U_2$	$\frac{{\lambda }_2{\lambda }_3}{({\lambda }_1+{\lambda }_3)({\lambda }_1+{\lambda }_2)}$	$(3,2)$	$X_1<X_2$	$I_{132}$
$U_3<U_2<U_1$	$\frac{{\lambda }_1{\lambda }_2}{({\lambda }_2+{\lambda }_3)({\lambda }_1+{\lambda }_2)}$	$(1,2)$	$X_1>X_2$	$I_{321}$
$U_2<U_3<U_1$	$\frac{{\lambda }_1{\lambda }_3}{({\lambda }_2+{\lambda }_3)({\lambda }_1+{\lambda }_2)}$	$(1,3)$	$X_1>X_2$	$I_{231}$