MathDB

For

i=0,1,\dots,5

let

l_i

be the ray on the Cartesian plane starting at the origin, an angle

\theta=i\frac{\pi}{3}

counterclockwise from the positive

x

-axis. For each

i

, point

P_i

is chosen uniformly at random from the intersection of

l_i

with the unit disk. Consider the convex hull of the points

P_i

, which will (with probability 1) be a convex polygon with

n

vertices for some

n

. What is the expected value of

n

Problem Statement