A Probability Path pp 1-27 | Cite as

# Sets and Events

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## Abstract

The core classical theorems in probability and statistics are the following:

*The law of large numbers (LLN)*: Suppose \(\{X_n, n \geq 1\}\) are independent, identically distributed (iid) random variables with common mean \(E(X_n) = \mu\). The LLN says the sample average is approximately equal to the mean, so that$$\frac{1}{n}\sum \limits^n_{i=1} X_i \rightarrow \mu.$$

## Keywords

Countable Union Symmetric Difference Finite Union Finite Intersection Monotone Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 2014