For a sequence of independent, identically distributed random variables with finite expected value, the running average of the first n of them converges in probability to that expected value as n grows. It is a weaker form of convergence than the strong law, and was the form first proved, by Jacob Bernoulli, for coin-flip type trials.
Facts
StatementThe weak law of large numbers (also called Khinchin's law) states that given a collection of independent and identically distributed (iid) samples from a random variable with finite mean, the sample mean converges in probability to the expected value 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Law of large numbers, Wikipedia
Sources
1. Weak Law of Large Numbers (Wikipedia)
Wikimedia FoundationForms section, Weak law subsection
The weak law of large numbers (also called Khinchin's law) states that given a collection of independent and identically distributed (iid) samples from a random variable with finite mean, the sample mean converges in probability to the expected value
History section
Khinchin showed in 1929 that if the series consists of independent identically distributed random variables, it suffices that the expected value exists for the weak law of large numbers to be true.
View the Source 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
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