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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-8,
author = {B. Kopoci\'nski},
title = {Random split of the interval [0,1]},
journal = {Applicationes Mathematicae},
volume = {31},
year = {2004},
pages = {97-106},
zbl = {1057.60020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-8}
}
B. Kopociński. Random split of the interval [0,1]. Applicationes Mathematicae, Tome 31 (2004) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-8/