Comparison of probability density functions for the sum of n dice to illustrate the central limit theorem (original) (raw)

Comparison of probability density functions for the sum of n dice to illustrate the central limit theorem Comparison of probability density functions, p(k) for the sum of n fair 6-sided dice to show their convergence to a normal distribution with increasing n, in accordance to the central limit theorem; illustrated by CMG Lee. In the individual probability distribution functions, the minima, maxima and mods are labelled. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution, shown in black. p(k) 0.18 0.16 0.14 0.12 0.10 0.08 0.05 0.04 0.02 0.00 k k n = 1 1 2 3 4 5 6 1 / 6 n = 2 2 12 7 1 / 6 n = 3 3 18 10,11 1 / 8 n = 4 4 24 14 73 / 648 n = 5 5 30 17,18 65 / 648