Difference between revisions of "Law of large numbers"
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[[Bulletin of theAmerican Mathematical Society, v.50, No.3, July 2013, p.373-390. |
[[Bulletin of theAmerican Mathematical Society, v.50, No.3, July 2013, p.373-390. |
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</ref>. |
</ref>. |
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| − | $$ |
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| + | $\displaystyle |
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\lim_{n_\rightarrow \infty |
\lim_{n_\rightarrow \infty |
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\frac{1}{\ln(N)} |
\frac{1}{\ln(N)} |
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\sum_{n=1}^{N} |
\sum_{n=1}^{N} |
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\frac{1}{n} |
\frac{1}{n} |
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| − | \mathbbI_{ |
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| − | \{ |
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... |
... |
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| − | \} |
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| − | } |
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=\erfc(t) |
=\erfc(t) |
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| − | + | $ |
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==References== |
==References== |
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Revision as of 18:03, 6 July 2013
Law of large numbers, or Bernoulli law of large numbers is theorem from the course of [theory of probability.
The formulation of the theorem is attributed to Jacob Bernoulli [1].
$\displaystyle \lim_{n_\rightarrow \infty \frac{1}{\ln(N)} \sum_{n=1}^{N} \frac{1}{n} ... =\erfc(t) $
References
- ↑ Manfred Denker. Tercentennial anniversary of Bernoulli's law of large numbers. [[Bulletin of theAmerican Mathematical Society, v.50, No.3, July 2013, p.373-390.