Generalization To Digits Beyond The First
It is possible to extend the law to digits beyond the first. In particular, the probability of encountering a number starting with the string of digits n is given by:
(For example, the probability that a number starts with the digits 3, 1, 4 is log10(1 + 1/314) ≈ 0.0014.) This result can be used to find the probability that a particular digit occurs at a given position within a number. For instance, the probability that a "2" is encountered as the second digit is
And the probability that d (d = 0, 1, ..., 9) is encountered as the n-th (n > 1) digit is
The distribution of the n-th digit, as n increases, rapidly approaches a uniform distribution with 10% for each of the ten digits.
Read more about this topic: Benford's Law
Famous quotes containing the words the first:
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