Strong Law of Large Numbers

The arithmetic mean of 1/n ∑ X_i 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.