Using the plugin stattest.dll, we estimate our problem with a simulation.
We computed for each point in the graph the N stones to M boxes problem times. Each time, we looked if we were able to cover the domain M with at least one stone and we averaged to get the probability.
Syntax for the plugin is:
[M],[N],[number of attempts],throwNstonestoMboxesThe plugin gives two probabilities back:
[probability that all cells are occupied], [1-(average coverage probability)]
The first probability is . The numbers fit our formula and the approximation with .
Figure 7: Probability to cover entire domain with at least one stone
In the second probability, we looked at what percentage of the domain was not covered with at least one stone through all realizations of the experiment. The graphs shows that the uncovered domain decreases independently from the size of our problem, in respect to .
Figure 8: Average failure probability in respect to coverage