Probability Theory pp 101-127 | Cite as

# Moments and Laws of Large Numbers

Chapter

The most important characteristic quantities of random variables are the median, expectation and variance. For large *n*, the expectation describes the typical approximate value of the arithmetic mean (*X*_{1} + … + *X*_{ n })/*n* of i.i.d. random variables (law of large numbers). In Chapter 15, we will see how the variance determines the size of the typical deviations of the arithmetic mean from the expectation.

## Keywords

Poisson Process Independent Random Variable Monotone Convergence Theorem Geiger Counter Real Random Variable
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© Springer-Verlag London Limited 2008