Fix $n$ a (small) integer.

Let $N$ be a (big) integer. Consider $N$ random points in the $n$-dimensional unit cube $[0, 1]^n$. The $N$ points are independently uniformly distributed.

Define $V(N)$ to be the expectation of the number of extreme points of the convex hull of the $N$ points.

Question: when $N$ grows to infinity, how fast does $V$ grow?

For $n = 1$, one has $V = 2$;

For $n = 2$, my intuition suggests $V \simeq N^{1/2}$, but I'm not quite sure;

Similarly, for general $n$, my intuition suggests $V \simeq N^{(n - 1)/n}$.

Are there known results on this problem or similar problems?