For a sequence of independent, identically distributed random variables with finite expected value, the running average of the first n of them converges, with probability one, to that expected value as n grows. It is one of the two central laws of large numbers underlying the intuitive link between probability and long-run frequency.
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StatementThe strong law of large numbers (also called Kolmogorov's law) states that the sample average converges almost surely to the expected value 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Law of large numbers, Wikipedia
Source Law of large numbers, Wikipedia
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1. Strong Law of Large Numbers (Wikipedia)
Wikimedia FoundationForms section, Strong law subsectionQuote, Forms section, Strong law subsection
The strong law of large numbers (also called Kolmogorov's law) states that the sample average converges almost surely to the expected value
2. Law of large numbers, Wikipedia
In Group: Probability Theory, Lead section
In probability theory, the law of large numbers is a mathematical law
Proved By: Jacob Bernoulli, Lead section
law of large numbers (for a binary random variable) was first proved by Jacob Bernoulli. It took him over 20 years to develop a sufficiently
Proved By: Andrey Kolmogorov, Lead section
variables having an expected value (like the weak law). This was proved by Kolmogorov in 1930. It can also apply in other cases. Kolmogorov
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