converges in probability to 0. A strong law of large numbers is a statement that (1) converges almost surely to 0. Thus, if the hypotheses assumed on the sequence of random variables are the same, a strong law implies a weak law. We shall prove the weak law of large numbers for a sequence of independent identically distributed L random variables, and the strong law of large for the same hypothe...

Benford’s law predicts the frequency of the first digit of numbers met in a wide range of naturally occurring phenomena. In data sets, following Benford’s law, numbers are started with a small leading digit more often than those with a large leading digit. This law can be used as a tool for detecting fraud and abnormally in the number sets and any fabricated number sets. This can be used as an ...

at the same time, the mean chance of the contrary event F will be the sum of the fractions 1− p1, −− p2, . . . 1− pμ , divided by μ; and by designating it by q′, one will have p′+q′ = 1. This being, the one of the general propositions, which we wish to consider, consists in this that if one calls m and n the numbers of times that E and F will arrive or are arrived during the series of these tri...