论文标题
一个简单的多重整体解决方案，解决了破碎的棍子问题
A Simple Multiple Integral Solution to the Broken Stick Problem
论文作者
论文摘要
将封闭间隔$ [0,1] $视为棍子。分区$ [0,1] $ to $ n+1 $不同的间隔$ i_1，\ \ dots \，i_ {n+1}，$其中$ n \ geq 2，代表较小的棒子。经典的破碎棍子问题要求找到这些较小棍子的长度可以是带有$ n+1 $侧面的多边形的侧面长度的概率。我们将通过使用多个集成，证明此概率为$ 1- \ frac {n+1} {2^{n}} $。
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 a polygon with $n+1$ sides. We will show that this probability is $1-\frac{n+1}{2^{n}}$ by using multiple integration.
