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SticiGui Law of Large Numbers Demonstration  

The Law of Large Numbers says that in repeated, independent trials with the same probability \(p\) of success in each trial, the chance that the percentage of successes differs from the probability \(p\) by more than a fixed positive amount, \(\epsilon > 0\), converges to zero as the number of trials \(n\) goes to infinity, for every positive \(\epsilon\).

Although the chance of a large difference between the percentage of successes and the chance of success gets smaller and smaller as \(n\) grows, nothing prevents the difference from being large in some sequences of trials. The assumption that this difference always tends to zero, as opposed to this difference having a large probability of being arbitrarily close to zero, is the difference between the Law of Large Numbers, which is a mathematical theorem, and the Empirical Law of Averages, which is an assumption about how the world works that lies at the base of the Frequency Theory of probability.

Resource URL: http://statistics.berkeley.edu/~stark/Java/Html/lln.htm

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Subject classification(s): Univariate Distributions | Probability | Statistics and Probability

Creator(s): Phil Stark

Contributor(s): Phil Stark

This resource was cataloged by Ivo Dinov

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