Law of large numbers (1713)

Law of large numbers was proven by Swiss mathematician Jakob Bernoulli (1654-1705).

This is the fundamental principle of statistics that the sequence xn/n tends to p where the random variables xn have common mean p. This implies that the relative frequency of an event of probability p tends to p as the number of trials tends to infinity.

The weak law of large numbers asserts that the limit holds in measure by use of the weak convergence defined by Ernst Fischer (1875-1959); and the strong law of large numbers asserts that the limit holds point-wise by use of the strong convergence defined by Friedrich Riesz (1880-1956).

These are correct versions to replace the law of averages; the erroneous idea that after repetitions of one outcome the others become more likely.

T W Anderson, An Introduction to Multivariate Statistic Analysis (New York, 1972)

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