distance between two random poisson points

Question

Consider n random poison points which are distributed according to parameter $\lambda$. Two random points are chosen. Is it true to say CDF of the distance between two points equals to: $$F_{d}(x)=\frac{\sum\limits_{k=1}^{k=n}\left(1- \sum\limits_{l=0}^{k-1} \frac{\left(\lambda x \right) ^{k}}{k!}\right) e^{-\lambda x}} {n}$$