Random split of the interval $[0,1]$
Volume 31 / 2004
Applicationes Mathematicae 31 (2004), 97-106
MSC: Primary 60F05; Secondary 60J10.
DOI: 10.4064/am31-1-8
Abstract
We define two splitting procedures of the interval $[0,1]$, one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.
