He then defines a random sequence as one such that every infinite subsequence selected by an admissible place selection retains the same relative digit frequencies as in the original sequence (so one cannot select a biased subsequence, indicating that this is a genuine property of stochasticity).
Given that the range of weights (500 4500 kg) is much greater than the putative digit preferences (0 100 g), this is a reasonable approximation and only small biases in digit frequencies can be accounted for by the non-uniform distribution of birth weights, unlike the situation in other digit preference studies, for example, age.
Borel's theorem is that B has measure one; almost all infinite sequences are, in the limit, unbiased with respect to digit frequency.
We illustrate the idea using Martin-Löf's (1966: 604) example of the property of large numbers (having a digit frequency equal to ½).
The property of large numbers shows that almost all infinite binary sequences have limit digit frequency ½, but says nothing about how quickly this convergence happens or about the statistical properties of the initial segments.
Using HLA-DRB1 four-digit frequencies that have been observed in patients with GCA to infer the amino acid residues in the GCA cases could lead to a biased analysis with inflated false-positive rate.
Eligible women who were residents of Marin County diagnosed with breast cancer in 1997 99 and women without breast cancer obtained through random digit dialing, frequency-matched by cases' age at diagnosis and ethnicity, participated in either full in-person or abbreviated telephone interviews.
As an example, for the digit 7 relative frequencies in the first 10 i, i = 0, 1, 2, 3, 4, 5, 6, 7 digits are 0, 0.095 0.097, 0.100250.09985, 0.1000207.1000207, which seem to be approaching 1 / 10 at rate predicted by the probability theory for random digits, i.e., a speed approximately proportional to 1 / n.
This study reports on the development and validation of new 'high frequency' digit triplet (HF-triplet) and CVC (HF-CVC) tests in British English with increased sensitivity for detecting high-frequency hearing loss.
Controls were identified using list-assisted random digit dialing and frequency matched to patients on race, age, and county of residence.
Better performance was observed for all subjects in forward digit span (low frequency stimulus type) than reverse.
