I am familiar with the Coupon Collector's problem. But what if instead coupons are distributed by a universal hash function? In other (more formal) words, if you hash set $S$ with function $h$ to buckets $B$, how big should $S$ be such that every bucket in $B$ is nonempty? This paper states that hashing $2n^2$ elements to $n$ buckets makes every bucket receive an element with probability $>1/2$. Why is this the case?
The paper is retrieved from https://www.brics.dk/RS/97/16/BRICS-RS-97-16.pdf