Question 90
A collection $\mathcal{S}$ of $10000$ points is formed by picking each point uniformly at random inside a circle of radius $1$. Let $N$ be the expected number of points of $\mathcal{S}$ which are vertices of the convex hull of the $\mathcal{S}$. (The convex hull is the smallest convex polygon containing every point of $\mathcal{S}$.) Estimate $N$.
An estimate of $E\gt 0$ will earn $\max (\lfloor 22-|E-N|\rfloor, 0)$ points.
Proposed by: Shengtong Zhang
An estimate of $E\gt 0$ will earn $\max (\lfloor 22-|E-N|\rfloor, 0)$ points.
Proposed by: Shengtong Zhang