Institute of Mathematics > Mathematics interactive > Stochastics > Strong Law of Large Numbers

Strong Law of Large Numbers

The arithmetic mean of 1/n ∑ Xi from i.i.d. integrable random variables converges almost surely to the expected value EX1. To illustrate this random numbers are generated according to the selected distributions (this corresponds to an observation of X1, X2 ...).

The right illustration shows the (count) desity of the distribution and the relative frequencies of the simulated values. On the left, the red line marks the expected value E[X1], the green dots show the course of the arithmetic mean of the random numbers.

Mean value and expected valueDensity and sample values
Distribution family
 
Distribution parameters
 
Sample
 
 

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