A Simple Multiple Integral Solution to the Broken Stick Problem

10 Jan 2020
•
Kaushik Vivek

Regard the closed interval $[0,1]$ as a stick. Partition $[0,1]$ into $n+1$
different intervals $I_1, \ \dots \ , I_{n+1},$ where $n \geq 2,$ which
represent smaller sticks...The classical Broken Stick problem asks to find the
probability that the lengths of these smaller sticks can be the side lengths of
an $(n+1)$-gon. We will show that this probability is $1-\frac{n+1}{2^{n}}$ by
using multiple integration.(read more)