Suppose I have some probability distribution with density function $p(x)$ and I draw $n$ samples from it. Then, I randomly toss out some fraction of those samples $k$ and look at the remaining samples.
Can I characterize the remaining samples? As $n\rightarrow\infty$, is there a pdf that describes them? My intuition is that probability density would move toward the tails.
There's no reason for the pdf of the selected samples to be different than the original n samples if the initial n samples were taken randomly and the k samples that were removed were also selected randomly. It is equivalent to having taken n-k samples initially.