Borel's law of large numbers
- Borel's law of large numbers
Roughly speaking, Borel's law of large numbers, named after Émile Borel, states that if an experiment is repeated a large number of times, independently under identical conditions, then the proportion of times that any specified event occurs approximately equals the probability of the event's occurrence on any particular trial; the larger the number of repetitions, the better the approximation tends to be. More precisely, if "E" denotes the event in question, "p" its probability of occurrence, and "Nn"("E") the number of times "E" occurs in the first "n" trials, then with probability one,
:
This theorem makes rigorous the intuitive notion of probability as the long-run relative frequency of an event's occurrence. It is a special case of any of several more general laws of large numbers in probability theory.
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