Difference between revisions of "Law of large numbers"
Jump to navigation
Jump to search
m (Text replacement - "\$([^\$]+)\$" to "\\(\1\\)") |
|||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | [[Law of large numbers]] |
+ | [[Law of large numbers]] is theorem from the course of [theory of probability. |
| + | The theorem states that the sum of independent identically distributed random variable |
||
| + | approaches the normal distribution. |
||
| − | The |
+ | The rate of this approach is determined by the |
| + | '''[[Bernoulli law of large numbers]]''' |
||
| + | (The formulation of the theorem is attributed to [[Jacob Bernoulli]] ) |
||
<ref> |
<ref> |
||
Manfred Denker. Tercentennial anniversary of Bernoulli's law of large numbers. |
Manfred Denker. Tercentennial anniversary of Bernoulli's law of large numbers. |
||
| Line 12: | Line 16: | ||
</ref>. |
</ref>. |
||
| + | <!-- |
||
| − | + | \(\mathbb P\) |
|
For some reason, the formula typing below fails: |
For some reason, the formula typing below fails: |
||
| − | + | \(\displaystyle |
|
| − | \lim_{ |
+ | \lim_{n\rightarrow \infty} |
\frac{1}{\ln(N)} |
\frac{1}{\ln(N)} |
||
\sum_{n=1}^{N} |
\sum_{n=1}^{N} |
||
| Line 23: | Line 28: | ||
... |
... |
||
=\erfc(t) |
=\erfc(t) |
||
| + | \) |
||
| − | $ |
||
| + | !--> |
||
| − | |||
==References== |
==References== |
||
<references/> |
<references/> |
||
Latest revision as of 18:44, 30 July 2019
Law of large numbers is theorem from the course of [theory of probability. The theorem states that the sum of independent identically distributed random variable approaches the normal distribution.
The rate of this approach is determined by the Bernoulli law of large numbers (The formulation of the theorem is attributed to Jacob Bernoulli ) [1].
This article is to deal with some strange behavior of MathJax. While the technical error is analysed, use wikipedia [2].
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.
- ↑ http://en.wikipedia.org/wiki/Law_of_large_numbers