Category:Kolmogorov's Law
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This category contains pages concerning Kolmogorov's Law:
Let $P$ be a population.
Let $P$ have mean $\mu$ and finite variance.
Let $\sequence {X_n}_{n \mathop \ge 1}$ be a sequence of random variables forming a random sample from $P$.
Let:
- $\ds {\overline X}_n = \frac 1 n \sum_{i \mathop = 1}^n X_i$
Then:
- $\ds {\overline X}_n \xrightarrow {\text {a.s.} } \mu$
where $\xrightarrow {\text {a.s.} }$ denotes almost sure convergence.
Source of Name
This entry was named for Andrey Nikolaevich Kolmogorov.
Pages in category "Kolmogorov's Law"
The following 3 pages are in this category, out of 3 total.