If there are $16$ 8$ random points in the plane whose horizontal coordinate and vertical coordinate are uniformly distributed on the open interval $\left(0,1\right)$, what is the expected largest size of a subset in which the points form the vertices of a convex polygon? Thanks!

If there are $16$ random points in the plane whose horizontal coordinate and vertical coordinate are uniformly distributed on the open interval $\left(0,1\right)$, what is the expected largest size of a subset in which the points form the vertices of a convex polygon? Thanks!