# Central Limit Theorem

(redirected from Lyapunov condition)
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## Central Limit Theorem

The Law of Large Numbers states that as a sample of independent, identically distributed random numbers approaches infinity, its probability density function approaches the normal distribution. See: Normal Distribution.

## Central Limit Theorem

In statistics, a theory stating that as the sample size of identically distributed, random numbers approaches infinity, it is more likely that the distribution of the numbers will approximate normal distribution. That is, the mean of all samples within that universe of numbers will be roughly the mean of the whole sample.
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Theorem 8 shows that the w groups of random variable sequences [Y.sub.ki] (1 [less than or equal to] K [less than or equal to] [omega]) satisfy the Lyapunov condition. That is, the sum of each layer data [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] obeys normal distribution.

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