Broken Stick Rule

number of pieces

10

expected size of largest piece = 0.2929

The broken stick rule refers to the expected sizes of ordered spaces created by random points on a line. If the unit interval is divided into

n

spaces by

n-1

random points, the expected size of the

i

th

largest space is

n-i

∑

j=0

1

n-j

n

. The broken stick rule has been suggested as an explanation for the apparent power law behavior of firm sizes and market shares.