On the distribution of monochromatic complete subgraphs and arithmetic progressions

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.