Linear combinations of independent random variables have been extensively studied in the literature. Xu & Hu  and Pan, Xu, & Hu  unified the study of linear combinations of independent random variables under the general setup. This paper is a companion one of these two papers. In this paper, we will further study this topic. The results are further generalized to the cases of permutation invariant random variables and of independent but not necessarily identically distributed random variables which are ordered in the likelihood ratio or the hazard ratio order.