Random split of the interval $[0,1]$

Volume 31 / 2004

B. Kopociński Applicationes Mathematicae 31 (2004), 97-106 MSC: Primary 60F05; Secondary 60J10. DOI: 10.4064/am31-1-8


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.


  • B. KopocińskiMathematical Institute
    Wrocław University
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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