Let's say we have a dataset $D$ with $N$ rows and $M$ columns. Each column is a feature. And for each feature $X_1, X_2,..., X_N $~ iid $F_p$ where $F_p$ is the distribution for feature p. Now let's do a random sampling which samples $K$ rows from $D$ and let's denote this sample as $D^K$.
So my question is: in $D^K$, for each feature p, does it follow the same distribution of this feature p in $D$? My instinct is that when $M$ is a large number, if $K$ is not large enough, then it cannot guarantee every feature p in $D^K$ has the same distribution as that in $D$. But I don't know if it is right. If it is right, how can I determine the minimum $K$ that's required?