Thomas Liggett - University of California, Los Angeles (UCLA), Mathematics A polynomial with positive coefficients is said to be strong Raleigh (SR) if all of its roots are real, and hence negative. A random variable X with values 0,1,…,n is said to be SR if its generating polynomial is SR. Motivated by an attempt to prove a multivariate CLT for SR random vectors, Ghosh, Liggett and Pemantle (2017) raised the question of the extent to which jkX can be well approximated by an SR random variable when X is SR. Using the technique of polynomials with interlacing roots, we proved in that paper that ⌊1kX⌋ is such an approximation if j=1. It turns out that ⌊2kX⌋ is very far from being SR. Nevertheless, I will show that it satisfies an equally useful property known as Hurwitz. I will then speculate about corresponding properties of ⌊jkX⌋ when j≥3. In particular I will consider two families of properties Pj and Qj for j≥1. For these properties, P1=Q1=SR and P2=Q2=Hurwitz. Unfortunately, P3≠Q3, but we can prove that ⌊jkX⌋ is Qj. The more useful property is Pj.