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TU-Clausthal Institute of Mathematics
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Strong law of large numbers

The arithmetic mean 1/n ∑ Xi of i.i.d. integrable random variables almost certainly converges to the expected value EX1. To illustrate this, random numbers are generated for the distributions that can be selected via the selection box (this corresponds to an observation of X1, X2...).

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