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Random split of the interval [0,1]

B. Kopociński — 2004

Applicationes Mathematicae

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.

Random errors in analysis of population growth

B. Kopociński — 1999

Mathematica Applicanda

The model of bacteria population growth in terms of the logistic equation is considered assuming the plate dilution technique of viable counting in the experiment and random errors in data. For example the Fisher test states that the growth equation and the standard description of the random errors are rejected. The extended analysis of errors is presented in terms of an operator which enables to separate three types of random elements: the stochastic growth of dilutions and sampling. On the basis...

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