Sets and Events

  • Sidney I. Resnick
Part of the Modern Birkhäuser Classics book series (MBC)


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
$$\frac{1}{n}\sum \limits^n_{i=1} X_i \rightarrow \mu.$$


Countable Union Symmetric Difference Finite Union Finite Intersection Monotone Sequence 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Sidney I. Resnick
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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